There is a bee spray you can mix in a pump up and reach the higher carpenter bee holes. This worked for me.

It’s most likely a common wall. I’m extremely worried about neighbors hearing extremely private noises.

The least expensive option is going to be to create white noise.

Otherwise, you'll need some type of sound insulation and dense pack cellulose might be able to be retrofitted into the wall cavity. But determining your level of performance expectation is the hard part. How perfect do you expect it to be? Is this a common wall to another unit, or all enclosed within yours? It makes a difference.

Rockwoll Insulation is a great way stop reduce sound.

I have seen a lot of great DIY carpenter bee traps that fill up with bees. I have friends that say the traps keep them out of the house. 

https://www.pinterest.com/explore/carpenter-bee-trap/

Most hardwood floors can be cleaned easily with a microfiber mop and a natural cleaner such as Mohawk's Floorcare Essentials Hardwood and Laminate Cleaner. It is all natural, works great and doesnt leave a hazy film on the floor. As with any product you use, make sure you test it first in a small area.

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.

Yes you can. However every condominium association has its owns rules and regulations.

You will need to contact the DC Zoning Department to get information regarding your property setbacks. Once you get the information on restrictions or limitations in your area there can be a few ideas such as a closed in porch or even sunroom. I have a relative who lives on S Street and he built a two level deck on his townhouse. The areas, if similar to his, are somewhat small and narrow but can be manageable for new construction. Good luck on your project!

I would presume that there are restrictions in Washington which require the approval of an Urban Design Commission for any archietectural modification to an older structure. Such organizations operate with guidelines that are unique to your area.

I would suggest that you contact your local Building Department. Provide them with the name of your neighborhood and inquire of them  "what if any restrictions limit your options".

Insulation is insulation regardless of type.  Whatever the R-Value per inch of the specific material is, times the number of inches, will equal the total R-Value.  We are looking for R-49 to be Energy Star. 

If the roof is not vented or we are talking about a hot roof deck, that is another consideration. 

The floors in your home, while insulation will certainly mitigate this delta, will be different temperatures as the laws of thermodynamics are universal. 

Get the insulation in the attic to R-49, seal the ductwork, seal the top plates, etc. and you will be good. 

R-49 also ventilation is very important to have soffit vent as well as roof vent to keep the attic cool and dry.

Insulation may not be the only thing you need.  It is also important to have air flow through the attic.  this is best accomplished by eave or soffit venting and ridgevent.

According to most building codes, you need one square foot of vent area for each 150 square feet of attic floor space. The minimum is one square foot for every 300 square feet of attic floor space if there is a vapor retarder or the space is balanced between the ridge and intake vents. A balanced ventilation system means about 50 percent of the required ventilating area should be provided by exhaust vents in the upper portion of your attic with the remaining 50 percent provided by intake vents.