I'd like you to check these few sentences for me. Thank you very much.

1) I'd hate to lose (and not losing) my ring because it was my grandmother's.
2) I use the internet to do school research and to look up information I need for school.
3) I'm a Tim subscriber. I subscribed Tim last year. I don't have to top up my cell phone myself since it tops up (I don't know if this verb is possible) automatically.
4) I recharge it every two days.
I like listening to music on earphones when I'm jogging.
5) Can you say: I said to John that I was going away.
Or it is better: I told John that I was going away.

1. Sentence is fine, and "to lose" is correct, yes.

2. OK

3. I'm not sure what "Tim" is, and I'm semi-unsure of what "tops up" means. But the only addition I'd make is the word "to" in front of "Tim" in the second sentence.

4. OK

5. You can say it either way, but the second phrasing is better -- simpler.