Answers

I have yet to survey a home that didn't need additional insulation and more importantly....air sealing. 

While HVAC systems are typically older in most homes that we audit, every home that I have ever been in leaks too much air and much, much more than is required.

Air Sealing and Insulation would be #1 and #2 on my list.  After that, items like HVAC and windows will jockey for position depending on the condition of both. 

Unfortunately, insulation and sound proofing is not required per code between conditioned spaces in this case.

It is also worthy of note that additional insulation between the floor will do very little to impact the noise tranmission as a majority is carried via vibrations on the framing. 

There are applications and techiques that can can be deployed.  All of them will require removal of the existing ceiling if you stay with a drywall finish.  You can run resilient channel in addition to sound de-coupling isolators. 

It is not an easy or cheap bullet fix in this case. 

Air sealing and insulation are the two biggest things you can do to globally improve the efficiency of the home. 

There are several articles on this application and I have yet to be in a home that didn't need it. 

Tightening up the envelope across the attic surface will lessen air infiltration at all the other areas of the home. 

They have places that you can rent goats from.  They are prolific eaters. 

This type of staining (algae as the other posters have said) will usually only happen on the North facing surface of the roof.  Same with condensation on your car glass.  Suprisingly, the North facing sky will actually remove heat from a substrate and thus make the roof surface colder.

Colder roof surface = condensing surface.  The moisture combined with the organic component will combine for a great growing surface (that the the rock dust organic component of the shingle).

It is not surprising that it is happeing more after you insulated the home.  By insulating (a good thing), you have reduced the heat sink between the roof and the conditioned space below and therfore made the roof colder in the process.  Colder roof...same as stated above. 

Plenty of roof washes out there that will handled most of this stuff and it does not mean the roof is cooked. 

I will have to disagree with the last answer.  Whether they work or not depends on the vegetation.  I don't care for the reverse curl systems because of their tendency to overshoot during heavy rains.  We use a grate style cover that keeps out 95% of the stuff and 99.99% of the stuff that forms clogs.  We haven't had one clog in 10 years and the system that we specify catches all the rain. 

+1

If you can amortize it into the long term loan on the home, it is a 100% no brainer.

Yes!!

Almost any mildewicide will do the trick.  Grout sealants all seem to work but I would go specifically to a tile shop to see what they recommend.  I think most sealers will work but application and prep are key. 

On the squirrel removal, best to call a trapper or get a trap. 

That area agains the home can be covered with some heavy guage counter flashing and sealed up prior to that with some fast setting mortar. 

John,

I must confess to never having seen that application. 

I am not sure the finish would look good or even hold up over the long term.  I would also be worried about the potential vapor retarder level interplay with what is behind the tile. 

The most often recommended window covering for efficiency is a cellular shade.

Please note that as you keep more of the interior heat from reaching the interior window surface, the potential for condensation will go up with that reduction in heat exposure as a result of the window's lower surface temperature.

Air sealing and insulation of the exterior top plates is critical to preventing that warm and moist air from warming the roof deck.

Attic ventilation is critical to keep that attic dry and as close to ambient air temperature.

Keep in mind that some ice dams are not preventable regardless of insulation and ventilation.  That being said, I would venture a guess that 90% of ice dams are the result of poor insulation and ventilation. 

Scott,

The easiest thing to do is check in the attic and look at the sheathing. If there is any mold growth, you can tread it with a proper mildewicide and make sure that the fan ducting is extended to vent through the roof or through the side of the home (i.e. to outside).

Good time to check the venting of the roof in general as well as look into any air sealing and insulation.

Don't worry about the mold having spread to the home and points further than the attic...it will not have as a result of a poorly routed bath fan.

If you are concerned about the mold while accessing the attic, have proper PPE (personal protection equipment) on to include a respirator that is effective against mold spores.

Don't disturb them until you treat them.

Cat smell or cat urine smell? 

If it is the latter, I have had success with Nature's Miracle.  If the smell is just the animal, that will diminsh with time and with changing out blinds, flooring, wall coverings, etc.