You may just as well leave translations to translators. See, when you have a good command of a language, there are numerous ways to say these things. For the majority of your questions there are no quick solutions that are going to sound natural outside some specific questions.

1) Just as well
I would stick to two solutions:
- "I'd better ...": when you are thinking about better use of your time. Use "лучше" or "Лучше бы" with a verb: "Нам лучше пойти домой. Не думаю, что он придёт". In this specific case you may use a sentence with "спокойно" instead, meaning "we should not worry and just go home" (i.e. "I am pretty sure nothing bad will happen if we just go home"). It would be "Мы можем спокойно отправляться домой. Не думаю, что он придёт". Usually "спокойно" means "calmly".
- "makes no difference whether you do this, or maybe something else": The use of "с тем же успехом". Not a safe solution, as it is going to sound unnatural when used inappropriate. Past events or grotesque recommendations work fine: "С тем же успехом мог ты мог бы выйти в трусах" - "You might have just as well go outside in your underwear"
2) might as well/ might just as well : sorry, I don't see how it is any different, given that the laguages are different and you'll have to turn to some kind of rephrasing anyway

3) We're equal.
I have no idea how you can use just one translation for this and still sound natural. Try "В этом мы похожи" (lit. "we're similar in this regard") or "Что-то общее у нас есть" ("At least we've got something in common")