Why don't you come camping with my soccer team?

[Brightsun]

Hi! ^^
I am an English teacher in middle school in Korea.
I found one sentence I don't understand in the textbook for the second-grade students. The following is the dialogue between M and S.
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M : Mike, sunmmer vacation is coming soon. Do you have any special plans?
S : So far i don't have any plans.
M : Really"
S : Yean, maybe I will just stay home and study Korean.
M : That's soundss good, but you have to get out, too.
S : Do you have any ideas?
M : In fact, I do. Why don't you come camping with my soccer team?
S : Camping? That sounds interesting.
M : My team will go to a mountain for one week.
S : I'd like to, but I have to stay home.
My grandfather will be here during vacation.
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Question 1, Is the phrase, come camping, used like in the sentence?
Is it right?
2. if the answer is yes, What's the difference between come camping and go camping?
3. What is the exact meaning of come camping?
4. For what occasion is come camping used?
4. My team will go to a mountain for one week. I think this sentence is unreasonable. in my opinion, it should be changed to ' My team will stay in a mountain for one week. or My team will go up a mountain for one week.' Am I right?
I'd appreciate your help. ^^

[Anglika]

Question 1, Is the phrase, come camping, used like in the sentence?
Is it right? Yes
2. if the answer is yes, What's the difference between come camping and go camping? "come camping" - be with us on a camping trip "go camping" - spending a little time camping [not specified with anyone]
3. What is the exact meaning of come camping? see above
4. For what occasion is come camping used? Inviting someone to come with you on a camping trip.
4. My team will go to a mountain for one week. I think this sentence is unreasonable. in my opinion, it should be changed to ' My team will stay in a mountain for one week. or My team will go up a mountain for one week.' Am I right? It is awkward. I would have thought that the person organising the trip will know which mountain and therefore the sentence should be "My team will be on the mountain for a week".