Hi Thammy,
1) Please, is the underlined order below, correct?
"It's a beautiful, big and great museum"
These three make an awkward combination. I think "great" is probably the problem. It's a big, beautiful museum. It's a terrific, big, beautiful museum. (Don't say "great big" because that sounds like it's very big insetadn of both big and great.)
2) - Is it also correct to write/say "coastal cities" for those that are spotted near the coast ?
You can certainly say "coastal cities" but I don't think you want to say "spotted." Do you mean "located" or "sited"?
3) What is the correct verb tense for this sentence:
" I have stayed for four weeks in 2007 and made new friends there."
(or)
"I stayed for four weeks in 2007 and made new friends there." 
Generally when you refer to a specific time in the past ("in 2007") you use simple past.
3b. (In both sentences I believe it's better to omit the preposition "for" to avoid 'cacophony', isn't it?)
The first "for" may be glided over. I stayed fuhfour. I wouldn't omit it outright.