1-When a card asks for random cards to be chosen, who chooses and how?
Examples: -Take The Shinies reads: Each other player discards two random cards.
-Brownie reads: After another player plays a card that affects
this minion, that player discards two random cards.
Does the player discarding choose? Does the player who played the card choose? Are they drawn at random? Or can you look through and choose the cards to be discarded?
It doesn't really matter who chooses, so long as it is random I.E. you can't look though them and decided, unless it specifies you can
2-Is there a limit to the number of special actions that can be played during the "Check For Scoring" phase? If I understand correctly, there is no limit and the current player gets to play specials first, am I right?
No, you are correct; no limit, with Special action rounds starting with the current player and continuing until all players pass sequentially.
3-Is there a limit to the number of actions played on a base?
No, no limit - Steampunks be smiling!
4-Cellular Bonding reads: Play on a minion. Choose an action on a minion. Ongoing: This card has the abilities of the chosen action.
If the chosen ability is no longer in play (ex: Minion with ability is destroyed), what happens to the minion with Cellular Bonding? Does he keep the ability?
Not as sure on this on, although I'd say it retains the effect of the action (it's not like a Mimic that actively copies a current aspect each turn).
5-Do cards that affect Actions "On a base", also include Actions played on Minions at that base?
No, only actions that specifically say "Play on a Base".
Hope this helps a tad