Hey, welcome to TPM, Liam! Enjoy your time here!
As for your question, yes, you can trade between FireRed/LeafGreen and Ruby/Sapphire/Emerald (more frequently referred to as FrLg and RSE, respectively). In order to evolve an Eevee by happiness, you'll need to do things that will make it happy. (It just makes sense!)
In general, a Pokemon's "Happiness level" can range from 0-255, with 255 being the maximum. This value is hidden, however; if you want to know where you are, you can either keep track of it or ask one of the girls in Verdanturf Town to give you a rough estimate.
All Pokemon that evolve through happiness do so once their happiness level reaches 220. Now, here are the things you can do to raise a Pokemon's Happiness level (thanks to a GameFAQs guide for the following info):
There are some items to help quicken happiness gaining. If you give your
Pokemon a Soothe Bell to hold, it will increase your rate of gaining happiness
by 50%.
If you catch a Pokemon in a Gorgeous Ball, you'll get:
- x2 regular happiness points from levelling up
- x2 regular happiness points from walking
- x2 regular happiness points from using them in an important battle
Next are all the ways of gaining (and losing) happiness
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Method |Effect |
================================================== ===========
Walk 256 steps |+1 for all happiness values |
Give vitimins |+5 in 0-99, +3 in 100-199, +2 in 200-254 |
Important battle|+3 in 0-99, +2 in 100-199, +1 in 200-254 |
Level Up |+5 in 0-99, +3 in 100-199, +2 in 200-254 |
Pokemon faints |-1 in all happiness values |
Energypowder |-5 in 0-199, -10 in 200-249 |
Heal Powder |-5 in 0-199, -10 in 200-249 |
Energy Root |-10 in 0-199, -15 in 200-249 |
Revival Herb |-15 in 0-199, -29 in 200-249 |
================================================== ===========
Note that Espeon and Umbreon evolve from Eevee when happiness reaches 220 during the day and night, respectively. Unlike in Gold/Silver/Crystal (GSC), however, you can't tell which is which just by looking at the screen, as the sky doesn't change to reflect night and day. The following times (going by the game's clock) are considered "day" and "night" in RSE:
Day (evolves to Espeon): 12 p.m. - 12 a.m.
Night (evolves to Umbreon): 12 a.m. - 12 p.m.
One more thing... there is one other way to get Espeon and Umbreon, but you'll need another game and some extra equipment to do it. On Pokemon Colosseum (for the Nintendo Gamecube), the main character starts out with both an Espeon and an Umbreon. With that game, a Game Link cable, and a Nintendo Gamecube, you can trade them to your GBA game. But that's a heck of a lot of extra equipment for just those two Pokemon, especially when there are other ways to get them. I wouldn't recommend it unless you want Colosseum for other reasons or you already have most of the extra devices I mentioned.
Anyway, sorry if that was a little lengthy. If you have any questions or need any clarifications, just ask. Have fun on TPM! ^_^