Old linoleum type tiles are common carriers, ceiling tiles, mastic, plaster, plaster board.  

For speed & convenience I only use the premixed mastic & grout as depending on ambient temperature the mixed powder stuff has been a big problem.

Let me tell you lots of my rentals got pretty back splashes for little more than the price of mastic and a few hours of work.   

There were many parts of south Shirley, Mastic and Mastic Beach that took a beating...  

Hello Teri,I am looking to start investing in Mastic Beach also and wanted to connect with you. 

I use thinset on all floor tiles, I only use mastic on backsplashes.

It runs about $40 but is the best they sell.I dont know what these corner pieces you speak or are but if they are tile they should be put down with thinset mortar if on the ground or mastic on the wall.It doesnt sound like you know what you are doing and it sounds like a small job.

(Pro tip: ONLY use thinset for the floor, NOT mastic.

tiling on the wall, it's best to use type 1 mastic.

I have never heard of Ductwork having to be replaced the system having to be replaced, yes. if the existing Ductwork leaks then look into sealing the joints with duct mastic ( do not use the grey duct tape) or us the silver duct tape. if the ducts are in the attic and bare metal try getting some duct insulation and wrapping them - just a couple of easy solutions.