Tell me please where you can find the end of the bounty.
If the thread does not mention the date, best way is to ask from telegram group, because every bounty now has a telegram group, but be careful because on some bounties, you cannot discuss bounty regrading questions on the main telegram chat, there's a different channel just for bounty questions, so before ask a question regarding bounties ask from the group whether you can or cannot ask about the bounty, when an Admin confirms, ask about the end date. that's the most accurate way.
And can I register in the project if half the time has passed?
Some bounties has participation limits, if the limit is not complete you can join, It's not a problem to join after passing half of the bounty, even if you can do one week, do it, it's always good to extend the number of tokens you have, expand your portfolio.