Hi!
I don't know a direct answer to question number one but I always found tucking to be a non-problem since you can almost always wear clothes that make it unnecessary. On the beach, I used to wear a beach skirt in the same fabric as the swimsuit. I googled beach skirt just to find an example and here is one:
http://www.smallest-bikin[...]arent=7
Hides everything and I think it looks great too.
Can't help you on question number 2, never wore a bikini before I had breasts that needed covering up.
About makeup and melting.. I'm no makeup specialist by any means but I think it's liquid foundation that cause the melting effect. When in the sun, your pores will open up and you will start to sweat and that sweat will mix with the foundation and it will "melt". At least I guess that's what happens.
Try using a mineral based foundation instead, I use "i.d. bareMinerals" which works fantastic for me (even mom started using it after I recommended it) :) . I think it has a sunscreen factor of about 20 or something too...
If you use a mineral based foundation, there is nothing that can "melt" although you will of course still get sweaty and your face will get shiny from it but hey, that's what it's like to be human. :)