check out or check
example
1. please come here to check/check out my work.
2. would you like to check/check out this list again
3. you can check/check out my phone you cant find anything what are you looking for.
4. have you check/check out this list
5. what are you checked /checked out on this list.

Question

check out or check
example 
1. please come here to check/check out my work.
2. would you like to check/check out this list again 
3. you can check/check out my phone you cant find anything what are you looking for.
4. have you check/check out this list
5. what are you checked /checked out on this list.

Answer

"check out" is really only used casually and it means something like "come look at this really cool/interesting thing".

I would say in all of the sentences you gave "check" works better but depending on the context "check out" might work as well in some.

The only time I can think of where "check out" isn't used casually, is when you "check out a book from the library".

Answer

"check" = "detect errors in"
"check out" = "look at"