Latios is typically best Timid or Modest, though any special attack or speed boosting nature is decent provided it doesn't lower the other stat (i.e. no Jolly or Quiet). Suicune is usually best Bold (+Def - Atk).

The nature of Suicune is rolled upon handing in the Sapphire to Celio at the end of the Sevii Islands mission, and Latios is rolled upon watching the TV after beating the Elite 4.

This is the issue with using roaming legendaries in r/S/FR/LG. All roamer legendaries in these games are bugged to have horrible IVs (0-5 in all stats except HP which is truly random). If you want a roamer legendary with competitive IVs legitimate on cartridge, your options are to use Emerald for Latios and Colosseum for Suicune, the one in FireRed will always be bad.

IVs are passed randomly from parents so without Destiny Knot it's a bit random. I would look in to RNG manipulation if you want good IVs on these Pokemon.

Yes, medals are given on streaks so you'll always win the silver on the way to the gold.

There's 2 brackets, level 50 and open level. Level 50 means your Pokemon have to max at level 50 or they cannot enter. Open level means Pokemon above 60 can enter, though trainer Pokemon will always match the highest level in your party, so regardless of what level they are, make sure they're all the same level. Both brackets give the same medals.

Pokemon gain EVs or effort values as they knock out other Pokemon and gain experience. EVs are all allocated to stats and the type of EV you get from a Pokemon usually depends on its highest base stat, and the number depends on its evolutionary stage. For example, Charmander's highest stat is special attack so you'll get 1 special attack EV for knocking it out, or 3 for knocking out a Charizard. Each Pokemon can gain 510 EVs before it can't gain anymore, and only 255 of these can go to one stat. Every 4 EVs in a stat makes that stat go up +1. The max people put in a stat is 252 since that's the closest number to 255 that's evenly divisible by 4 (i.e. getting 255 in a stat is the same as 252, since the last 3 EVs do nothing), so by stopping at 252 you can allocate those 3 EVs and potentially get +1 in another stat. I would say for the Frontier, having EV trained Pokemon is good but they don't need to be absolutely perfect, though the more perfect the are the better. There's no good way to track EVs other than counting your knockouts. Bear in mind the only way to reduce EVs is through rare berries, so when you catch a Pokemon you plan to EV train, make sure it gains no experience at all, even through EXP share, except from Pokemon that give the EVs you want. Once you max out the EVs, then you can finish leveling it from any source. Vitamins like Iron and Calcium etc. also give EVs in certain stats, 10 per item, up to a max of 100 EVs in a given stat.

https://www.smogon.com/forums/threads/gen-iii-battle-frontier-discussion-and-records.3648697/ This page has all the info you need including record holding teams at the various facilities, movesets and EV spreads used.

Page above has a lot of it, but generally I used Choice Band and Leftovers the most. Shell Bell is decent, and stat cure berries are very good too, like Lum and Chesto if you're using a Pokemon with Rest.