Entei cannot return after fainting in Pokémon Gold, Pokémon Silver, Pokémon Crystal, Pokémon FireRed or Pokémon LeafGreen however in the event of it being knocked out and fainting during the battle then it can return in Pokémon HeartGold, Pokémon SoulSilver, Pokémon Omega Ruby and Pokémon Alpha Sapphire you will need to defeat the region's League Champion before the fainted Entei will re-spawn.
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In Gold, Silver, Crystal, Fire Red, and Leaf Green, no. If you KO them, you'll never find them again on that game file. In any games starting from Generation IV, however, you can KO them as many times as you want, and they'll always come back…after you beat the Elite Four and Champion again, that is.
I haven't found any reliable sources, but I believe Raikou, Entei, and Suicune all come back after the Elite Four if you didn't already catch them.
Yes, Entei is a legendary Pokémon.yes
entei is a legendary so it won't evolve
Entei can learn TM22- Solarbeam.