Yes you can. later in the game Latias (or latios depending on which game you have) is attainable. Like mesprit in Pokemon diamond and pearl and like mesprit, latias and latios tend to flee.
You need to get the Eon Ticket. You can get it by mixing records with ruby or Sapphire that has an Eon ticket.
latias
Yes.
You can find latias on every route in hoenn.
To get Deoxys, you need the Aurora Ticket from a Nintendo Event. To get Latias, they are in the wild after you beat the Elite Four. To get Mewtwo, you need to trade from LeafGreen or FireRed.
You can try to complete your Pokédex.
It will be Level 40.
You can catch Latias
You just have to keep on trying to catch it
Yes, Pokemon Sapphire version is the version in which you can catch Latias. You can only find it once you have beaten the Pokemon League, then there is a report of a legendary red flying Pokemon in Hoenn. Latias appears randomly.
For Pokemon ruby you can catch the three regis, rayquaza, groudon, and latios/latias. In sapphire you can catch the three regis, rayquaza, kyogre, and latios/latias. However, in emerald you can catch kyogre, groudon, rayquaza, the three regis, and latios/latias.
Unless you have an eon ticket, Latias will be a roaming Pokemon in hoenn. This means that he could be anywhere, so you just need to hope he is on your route. If you use sweet scent, it is easier to find.