I'll Do my best to help you out!
-No matter "How' hot "it is", Koreans eat hotpot.
(a short cut to this phrase is eg: No matter what, korean's eat hotpot.)
-No matter "Where" we go, we can find a Starbucks. (you said it, Starbucks is "Everywhere" so be sure to add the where or the what"
-No matter where I go, I can adapt to life in there.(Great! you could drop the "in" but this is fine!)
-There "is" something in common between you and me.( another example would be, "We have a lot in common", or " We have a few things in common")
-Why "Hasn't" she taken a shower "yet"?? She should "have done" it "earlier". It "is" already 23:30!
I don't want "her to" "make" (maybe add "a lot") "of" noise!
-I forgot to have the cakes that I bought 2 days ago...
Do you think it is OK until next week?(Perfect!)
-I'm scared by the movie.(I got scared by the movie. Is it more natural???)
(this one can be tricky because it totally depends on When you are saying this. Technically both are correct or can be correct. it can also depend on who you are saying this too. However these are just -fine)
-The teacher is scary. She always keep an eye on us.(this is great as well. maybe scary is not the best word but this works just fine!)
-I don't want to get hurt by doing something dangerous.(Perfect)
-He got hurt by a car accident.( this is totally acceptable as well. this would be said in present tense. if you were telling someone, you would say," He "Was" hurt in a car accident)
-I was embarrassed when I fell on a road.( this is very cute and totally acceptable! Great job! I hope this helps you!)