I need to re-seal my bathtub. I removed all the old caulk because the
guy at Ace Hardware said that new material won't always make a seal
when added to old. Is this correct?

There are some gaps up to about 1/4" that need to be filled. Should I
first fill these gaps and let the caulk dry, then come back and make a
nice neat seam?

Finally, is there a type of caulk that has some chemical that will
prevent mildew? My wife says that if this stuff doesn't exist,
someone should be able to get rich from her idea.