I want to convert an RSD website design to Site Designer V3. Will all other Coffee Cup apps remain functional? I have pages built by Menu Builder, Responsive Slider, and Web Form Builders incorporated into my site. Will they all remain functional, or will modifications within them be required?

Have you sent in a support request for this, in addition to asking here on the Forums -- which aren't necessarily all that well covered by the "powers that be"?
imho that'd be a good idea
AND THEN please post the response you get from them here, as it's of general interest

Since you more than likely used a html element it should all be fine. Save a copy of your site and work on a different one just to be sure you can go back. I always save a copy after big updates to be sure I can get back what I originally had.

What powers, Russell ?

the managers and staff at CC -- the Forums are only "visited" by them, occasionally -- it's "staffed" by fellow users

I am only guessing here but as the other apps use rows and columns I assume you will have to convert them to fit with the new framework container etc as you would have to do with your rsd project file

You now use rows and columns just as in the actual foundation or bootstrap framework documentation on each of their websites. For instance you add a div container and assign it .row and add another container inside that and assign it .col. Same thing but just using the way its actually done by real Foundation or Bootstrap coders. You can have tons of layout classes and up to 12 regular style classes. The procedure is the same for the html elent which all the programs listed use the embed method.