While looking at our options, acoustical ceiling tile adhesive came up, which sounds like a perfect solution... if it works.

The thrid step is cleaning the area with soap and water and then treating with a residual chemical.

.- Soil extraction with low moisture steam- Application of fabric softener and color brighteners removes detergent residue according to manufacturers specifications, leaving fibers bright and soft with a silky feel.

Next is to start a business in the US with some of their "residual" cash.

I myself have been doing real estate for 3 years and now have decided to venture into acquiring rental properties for residual income for retirement.

The usual silicone being used as adhesive is always prevalent.

I know the stairs are wood because the carpet from the landing and two steps below it has been removed by someone other than me.Should all the carpet come off the stair and the adhesive be left?

One of the items on the list was to replace the kitchen floor (currently adhesive tile that is peeling up).

If you squeeze too hard on these you can get all kinds of residual issues.  

I assume your duplex was built before they widespread application of construction adhesive, so most likly you wont have to go down all the way.