I exist

1.7.10 is not a beta edition of Minecraft, you can use any version in between beta 1.5 and beta 1.7.3.

Yes, as long as the original jar files are ran. Playing different versions of indev and infdev were possible without the betacraft launcher anyway, but feel free to use what you like.

Achievements carry over worlds, and probably nobody will want to reset their copy after every single attempt, so it’s just not going to be possible.