For example I max out the beauty of a feebas in ruby/sapphire/emerald and trade it to firered. If I level up the feebas in firered, will it evolve?
Yes it will. I tried it on my LeafGreen copy using a Feebas I traded from Emerald with a high enough Beauty stat for it to evolve. Leve it up and you'll get a Milotic in front of your eyes. Source: Experience