1. comma needed
2. comma needed
3. comma needed
4. playing archery
6. "...because it was right on the beach."
1) My mum and I (not: I and my mum) went shopping and we bought a lot of souvenirs.
2) After a week (a week later) we came back home satisfied with this exciting experience.
There are slight differences in meaning. "After a week" seems to suggest you came back after being gone a week. "A week later would be used if you came back a week after doing the last thing you said.
I went on vacation. I started in Florida then went to Mexico. After a week I came back.
That means you started your week long vacation in Florida then went to Mexico. Your whole vacation was one week.
I went on vacation. I started in Florida then went to Mexico. A week later, I came back.
That usually means you spent a week in Mexico.
3) We put everything on a counter and then we walked through the gate that checks for metal.
The gate that checks for metal = the metal detector.
4) We took a bus to the hotel. I spent most of my time doing archery (playing archery)
Doing is better than playing. Practicing might be best.
5) We stayed at a campsite.
We always got a packed lunch from the hotel.
6) I liked going to the disco because it lay on the beach.
Sits on the beach.
We made new friends who came from Milan.
7) The hotel offered room service though it was very expensive.
Comma before though.
We went sightseeing in the city centre.
We went sightseeing downtown.
Tust her responses. I was typing and walking. Made a few mistakes.
I agree with Matt about these:
>>>the metal detector
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