1 He had better turn/turning himself in. 2 I'm sorry to hear/hear that you're ill.
3 What's the use of lock/locking the front
door if you leave the windows open?
4 I don't want to risk speeding/to speed -
it's against the law!
5 Jenny called the police to assist/
assisting her.
6 You mustn't to download/download
music without paying for it.

  hey mark! what are you going to do during half-term ?

            you (won't believe) it but i(visited) swizerland !

            really ? that's so exciting ! swizrland is great. i'm sure   you (loved) it.

            i think so, too. my family and i (stayed) at a hotel near the swiss alps.

              wow

              yeah, it great.i (played) in the snow every day.my brother and i also ) to learn how to ski.

              you're so lucky.i wish i could go with you.

                maybe you can. (should i ask) my parents ?

                definitely!

                ok, then. i (will talk) to them tonight.

                    great!

                  i think we should go to class now or we (will be) late 

                you're right. let's go 

1 I'm into tennis or basketball

2 I'm good at tennis, but I'm not good at basketball

3 do you prefer dancing or photography

4 I've gotta a camera, but i haven't got a laptop

5 is this your book or your brother's book?

6 i really like judo and taekwondo

ОБЬЯСНЕНИЕ

AND - That one action follows another in the chronological order.( AND - действие (или что либо другое) после другого в хронологическом порядке:

i like judo AND football)

BUT - The conjunction but is used to suggest a contrast. (Соединение, "но" используется, чтобы предложить контраст: i like: i would bye a game, but i haven't money.)

OR - The conjunction or is used to suggest that only one possibility can be realized.(используется когда даётся выбор или что-то вроде этого ( я так понял) : what do you prefer, smartphone or laptop?)