1. I have never been (in) to the UK.
In this case, been is the past participle of go and you go to the UK.
2. I didn't see (nobody) anybody there.
We don't use two negatives in one sentence in English. See this blog for more details!
3. I'll ask (to) him next time I see him.
You ask someone something.
4. When (I'll) I get home, I'll have a cup of tea.
We use the present tense after when in a sentence like this about the future. Think of the Beatles song: "Will you still love me when I'm 64?" Listen to the song here :)
5. Do you know where (does) he lives?
This is an indirect question, so you can't use the auxiliary verb 'do'.
6. I said to/told him that I was learning English.
You say something to someone and tell someone something.
7. There isn't (room) enough room for everyone in here.
Enough goes before a noun (but after an adjective - for example, the water isn't warm enough to swim)
8. I wouldn't (had) have done it if you hadn't asked me for help.
This is a 3rd conditional: If + past perfect, would + have + past participle. (In this particular sentence, the 'if' clause is second, but the meaning is the same)
9. When I was younger, we (hadn't) didn't have all the technology that exists today.
This is the negative form of the past simple, so we need the auxiliary verb.
10. I've been living in London (since) for three months.
We use since with a specific point in time, and for with a period of time, so you could change this sentence to "I've been living in London since July".