Answers:
Leaving it with a bucket underneath will be absolutely fine. what is the pipe feeding? is there any controlling valve that can control the leak?
Most of the taps now come with 10mm or 12mm but it does depend what kind of tap you get, you do have to be careful though on what tap you get as some taps are only suitable for pressurised systems. so it does depend on what system you do have as well
It could be a leak on the incoming main. have you checked this? or have you checked to make sure there isn’t any valves that need opening fully?
Yes you can use push fit on chrome pipe work. it wouldn’t look to good but it will work.