Sure, here are the correct forms of the verbs:

1. Vietnamese students love **going** picnic at the weekend. (go)
2. I hate **spending** all day on **going** fishing. (spend-go)
3. People in Britain love **drinking** tea with milk. (drink)
4. Do you like **listening** to music. (listen)
5. Does Anna fancy **watching** horrible movies. (watch)
6. I prefer **making** craft to **drawing** a picture. (make-draw)
7. Kate loves **hanging out** with her friends on her birthday. (hang out)
8. I detest **eating** fish. (eat)
9. Do you mind **turning** off the TV? (turn)
10. Does she adore **working** with handicapped students? (work)
11. Do you fancy **going** to the cinema this weekend? (go)
12. I detest **hunting**. I think it's cruel to the animals. (hunt)
13. Tom enjoys **doing** puzzles, especially Sodoku. (do)
14. I am fond of **taking** photos. In my free time, I usually go out and take photos of people and things. (take)
15. My sister is keen on **cooking**. She wants to become a chef in the future. (cook)