How much mana can I tap per turn?
There is no limit to the number of lands that you can tap per turn. For your other question, all of your tapped permanents will untap at the start of each of your turns, during the "untap" step.  

You have a few different important basic terminology mixed up though. Mana and Land are 2 different things. Land is a type of card, one that most commonly produces mana (but some lands do not produce any mana). Thus, "Forest" is not a type of mana, "Green" is a type of mana, and Forests are cards that produce Green mana when tapped.

Also, you do not need to pay mana to attack with creatures, including Arbor Colossus. You need to pay mana to cast Arbor Colossus (to out him from your hand into the battlefield), and to activate his "Monstrosity" ability, which gives him 3 +1/+1 counters.