They are all common in the UK, with the exception of number 7 which I am not familiar with, although the equivalent UK saying is also common.
1-To have a sweet tooth. To describe someone who likes sweets, cakes and sweet things in general.
2-To have a heart of gold. To describe someone who has a good underlying personality.
3-To have a good head on one's shoulders. To describe someone who is well-adjusted and not likely to get carried away by success, or dragged down by bad news.
4-To have one's hands full. Said when you have many things to do, or problems to resolve.
5-To have eyes in the back of one's head. Can be said about people who notice things a lot, or by people who are inattentive/who have been asked to look for something difficult about something that would be useful to them.
6-To have a big mouth. Said when someone says inappropriate things, or things at an inappropriate time. Very common, although a bit rude.
7-To have a green thumb.? Maybe something to with gardening? I think it must be American. If that is the meaning, in the UK we would say 'to have green fingers'.
8-To have one's head in the clouds. To daydream/be unaware of something.
If you have any doubts about the usage feel free to ask.