There was no pockets in his jeans or coat, so he had to hold it he said. 

You shouldn't need but one coat because you are just freshening up the white, but again matching what on the trim is important.  

Put down some anti slip strips, a non slip coating etc.

I forgot to mention the RS Means Estimator series available on Amazon for estimating material and labor unit coats. 

Do I need to put a top coat of something on there to protect them?

The more expensive, thicker medium filters actually restrict air flow and strain the air handler.

There is a special encapsulating coating for lead (Lead Block, for one), that's more like a liquid rubber, that can be used on certain surfaces only after the surfaces have been tested and the proper paperwork filed (the EPA loves it's paperwork).

What we have done in the past was to paint the floor with Kiltz Paint two coats then cover with pad and carpet.

If not good coverage, how many coats of paint did it take to cover?

If it comes up later you can always pull up those areas, skim coat, and paint again.