Yes, you can do that and no you don't need a particular font. The FSL when properly digitized will hold up your fonts.

Yes, but you have to make sure the stitches in the fsl design are close enough together to hold the letters. It may take trial and error, you won't know until you wash out the stabilizer. The denser the fsl stitches, the better the letters will work. Which design by cuties are you trying?
I have used some designs that have words already in them (then I know they work), I add my own words or design and change the stitch order to do the original words last. Then I just don't stitch the original words out. You could also leave them in order but then you have to remember to skip them during the sew out process.