Are we allowed to bid stock price after trading hours/office hours for the day? E.g. Sat/Sun. Will the price we bidded be in the queue for the next trading day?

Yes you submit order before or after market.

Yes, most platforms allow you to do that. It will just queue till the next trading day and execute if the price and quantity matches.

Here is everything about me and what I do best.

Yes, this is how i actually put my market orders. Looked at the closing bid/ask volumes then decide whats a reasonable price target that can be achieved on the next opening day.

Possible, but I won't really recommend it. You never know what happens at the opening bell.