Alphas are guaranteed at least 3 perfect IVs, 252 EVs in HP, and a Plus move that can normally only be learned through TM (referred to as an Alpha Move in the game's data).
Once you have unlocked the Judge function, it's very easy to confirm this by observing that a newly caught Alpha Pokemon comes with the "Best!" label on 3 stats and with the HP stat glimmering. The perfect IVs are likely random, in line with past special Pokemon with guaranteed perfect IVs, as catching the same Alpha Pokemon spawn multiple times results in individuals with different stat spreads. Alphas are distinguished from normal Pokemon by the red symbol besides their level and will always be size XL.
The Alpha Move is species-dependent and is not explicitly specified in-game but is noted in the personal.txt file for the game; I have organized this info into a list of all the Alpha Moves here. Note that not every Pokemon on this list can actually be legally obtained as an Alpha. Different forms of the same species have the same Alpha Move so redundant entries were removed.
The spawn rate for most Alpha Pokemon, discounting guaranteed spawns, is 5%. You can check the spawn rate for different Pokemon at different locations as well as their respawn times in this interactive map.
To clarify, a guaranteed spawn means that an Alpha Pokemon is guaranteed to be generated in that location, with the species being chosen randomly from a pool of possibilities. For some areas, there is only one possible option, so the same species will be spawned as the Alpha each time (e.g., Wild Zone 7's Alpha Fletchinder). However, some zones have guaranteed Alpha spawns that randomly select their species out of a variety of options. As an example, Gardevoir may be (but isn't necessarily) one of the 2 guaranteed Alphas in Wild Zone 20, but it can also appear normally, and the normal individuals have a separate 5% chance of being Alpha. You can see a list of only the guaranteed Alpha spawns here.
Alpha Pokemon drop a Seed of Mastery when defeated or captured, which can be used at the Justice Dojo to upgrade TM moves into Plus moves. They may also drop EXP Candy XS, S, M, and L, typically 1-3 pieces. The size and quantity of EXP Candy is random and has no set drop rate between species or individual Alpha spawns, but loosely scales with the strength of the Alpha Pokemon (i.e., higher level Pokemon tend to drop better rewards).
As an additional note, Alpha size classification is not the same as Pumpkaboo/Gourgeist variety, so Alpha Pumpkaboos/Gourgeists may still be considered to be of any size variety despite being denoted as XL.
Sources: Serebii, game data, personal experience
