Answers

Unfortunately, most new homes (particularly those built by developers) are built with little regard to quality and durability, by less-technically-savvy tradesmen at the lowest price point possible to appeal to a prospective buyer's sense of value. 

Should you be concerned?  Most of these sorts of issues are not conditions potentially leading to structural failure but rather finish failures and just generally less-than-desirable quality.

There are many industry specification references for quality, and likely your builder references a spec which is more forgiving of such issues.  For instance, a spec for drywall might say "out of level or line x inches in x feet" or simply "imperfections not visible under normal lighting conditions when viewed from x feet away".  You may want to research which specification may have been referred-to as quality guaranty when the home was sold.

Of course, this is a generalization and does not apply to all new construction.  One would want to engage a building professional to determine what may be happening in the particulars of your home.

Suggest that you find a reputable and skilled tile company.  If it was a vinyl pan, it may be possible (although not ideal) to tear out the floor and lowest 6-12" of wall tile to replace the pan.  It's really something that cannot be easily answered without a close professional examination of the particulars of your shower conditions.

Not much info here to make a determination.  Drainage issues can be tricky.  Depends on what the builder was engaged to do (was the contract specific about installation of a certain system, or was it a performance specification?).  If the contractor is a member of a local chapter of a trade association, such as the NAHB or NARI, they typically have ethics panels who can look at the issue and help you determine what you should have expected of your contractor.  Likewise, if your state has a Board for Contractors.

So many people today resort to the threat of negative online reviews, but please be careful how you use those.  That may be unfair to the contractor if there are contractual stipulations or specs he was to follow, and he may have done as contractually required, so trashing him online may not be warranted and can unjustly ruin the well-meaning contractor's means of livelihood.

You may also discuss your issue by engaging a legal professional.  Again, hopefully that professional can review the agreement and determine whether there is cause for pursuit - what obligations the contractor had to you, and whether he has met those or not.

As committed industry professionals, we want to know that our peers are dealing fairly with their clients.  I hope that you can come to understand rights and obligations in this case and resolve reasonably to your satisfaction.  

That is going to vary depending on where you live, the particulars of your home construction, as well as particulars of your planned "pop-top".  Here in Richmond, VA, the structure and exteriors, plus a window or two for a relatively narrow dormer runs in the $10-12,000 range... before you make interior renovations to the bathroom which presumably you may be seeking.

I am guessing that you may be interested in something wide than a 3-4 foot typical dormer.  Well, things become much more structurally complicated in a Cape roof, the wider this pop-top becomes.  As the roof loads become asymmetrical, beams and opposing side structural work will likely become involved (ie: you may have to add structure on the OTHER side of the house, and a beam at the peak of the roof... possibly posting-down to the foundation, to balance the load).  I have seen those go to $30,000+... again, before you start adding in the bath renovations below.  I know; sounds shocking but in order to maintain the structural integrity of your roof, these things may be neccessary.

We did this a year or so ago... sounds like what you are looking for.  Professionally constructed, I believe it was around $25K... Richmond, VA area.

That is Oriented Strand Board (OSB), typically used for sheathing.  Looks like it has been used exposed to weather, which is not its intended use.  There is no reasonable repair for that, other than replacement... with materials suitable for whatever the application might be.  Call a professional contractor.

Hard to tell for sure without a close look, but the roofing / waterproofing material looks like TPO, a single-ply roofing membrance.  It is not made for direct traffic, so appears someone has installed rubber pavers over it to protect the membrane.  Not an unusual application.  The membrane should have positive drainage to what appears to be scuppers, and any water falling on that balcony wants to be able to freely drain - meaning, any pavers installed should have a means of drainage on the underside.  Appears to me that these rubber walkpads really do not.

Have a professional roofer /waterproofing company take a look and work with you toward a solution.

Looks like this may have been someone's remedy for a deteriorated / rotten mud sill (the flat wooden plate which sits atop the foundation wall, upon which the joists bear).  If that is the case, it is possible that you might be able to remove the latter obstruction if one can restore the proper / original condition over the window.  That would want to be examined and undertaken by a professional.

As with any such thing, it is difficult to say for sure without a full on-site examination by a home imporvement professional with structural knowledge and experience in these types of repairs.

If the texture is a sparyed-on or roll-on application, there are strippers which will loosen and allow that to be scraped-off.  If it is drywall mud, it's not coming off so easily and you will spend many hours and create a huge mess sanding that down with an orbital sander... then potentially have to re-skim to get the surface ready to accept a good tile job.

We do a lot of backsplashes in existing homes. When the substrate (the surface to which the tile is to be applied) is not satisfactorily flat and smooth, we find that the quickest, cleanest, simplest solution is to remove the drywall and replace with new, moisture-resistant drywall.

Best answered by an attorney in your state.  In Virginia, we have a very simple legal filing called a "warrant in debt" which demands collection of such debts.  The process varies by state; hopefully there is a simple means to make your claim in Georgia, as the legal fees for filing and pursuing a full-blown lawsuit would likely well exceed the amount due back to you.

You may also consider filing a formal complaint with the professional licensure board.  In Georgia, that is a division of the Secretary of State.  See:

https://sos.ga.gov/index.php/licensing/plb/46

Misapplication of construction funds is a serious offense.  You will have to determine with your attorney whether you wish to pursue.

Georgia has a criminal statute, O.C.G.A. §16-8-15, titled: Conversion of payments for real property improvements. This statute provides a criminal cause of action if:

Any contractor, sub, or other person who with intent to defraud shall use the proceeds of any payment made to him on account of improving certain real property for any other purpose than to pay for labor or services performed on or materials furnished by his order for this specific improvement while any amount for which he may be or become liable for such labor, services, or materials remains unpaid commits a felony.

It would be difficult to prescribe a proper floor without specific knowledge of the conditions - how much moisture, and where is it coming from?  As well, it is always better to think of most anything in a home as a complete system.  By that I mean, proper preparation of the substrate (the concrete) including some manner of vapor / moisture barrier and/or other assembly to mitigate the moisture or its effects.

Additionally, consideration of the space function and/or requirements for use, aesthetics, etc.

There are moisture-resistant / moistureproof flooring materials such as LVT.  However, I am always concerned that these non-breathable coverings might trap moisture beneath, and create ideal conditions for mold growth - a problem which may be invisible but harmful.

I know... the concern and prospective solutions may seem simple, but - for the RIGHT answer, no so much.  Summarily, there are rarely easy answers to such questions without a more-thorough analysis which can / should really only be done by professional examination of the space.  For that, engage a professional designer / archtect and/or a well-educated remodeling professional. 

Flashing is an essential component for any window installation.  This is part of the system which protects from water intrusion and structural deterioration.  There may be gaps between your framing or old frame and replacment window frame.  These are typically filled with insulation (usually foam) for energy conservation and to prevent drafts.

Simplified / general answer above.  As with most construction / improvement details, doing it right depends on products, conditions, and is more complex than a two or three line answer can fully describe.  Your best assurance of having it done right is to engage a responsible and experienced contractor.