While it is promised that Israel will be regathered to the land of Israel from the places where they have been scattered. Will those people who attatch themselves to Israel be allowed in the land, when?

I'm not sure who are those which "attach themselves to the Jewish people" – if you mean converts – they will be part of the Jewish people. (See Isaiah 56, 2-8 and commentators there) If you mean non Jews that are good to the Jews – they will be rewarded and let to live in the land of Israel as a Ger Toshav if accepting the seven Noahide Mitzvot. (See Rambam Avodat Kochavim 10; 6)