We don't "close problems." These sentences don't make problems.
If there is an issue, we can close a case. So a problem, like a missing class on italki, becomes an issue, and "please make sure all problems have been solved", "please make sure all issues have been addressed" (worked on, solutions proposed, maybe still ongoing).
"Please make sure everything has been resolved." (Finished, 100% complete.)
"Please make sure that all cases have been closed." (For customer service problems.)
You don't close problems, you SOLVE problems. Or work on problems. Or address problems (when interpersonal or client problems need you talking to other people who may be angry, unknowledgable, or uninformed.)
Make sure and Make certain are both correct. "Make sure" is far more common. "Make certain" sounds formal, perhaps more British, but it isn't used at all.
Except for an item that has a Yes/No answer. You can make certain that the door was closed, email was sent, payment received. Yes/No type questions. It is a nice way of a boss saying "Please check again."
The "make certain" is polite, and implies that the other person is forgetful and needs to "make certain" that they didn't forget their wallet, or that they did it wrong, believe it's done, and the boss says they need to "make certain" that the job WAS done satisfactorally. It can be a way of being strict while sounding polite.
"Make sure" is much more common, a tad more informal, and very kind. "Make sure to visit the museum!" "Make sure you sign up for the free gift." "Make sure to try some food while you're here." "Make sure to visit NYC when you visit the United States." It can be a recommendation, an offer, an invitation. It also is a kind reminder: "make sure to tie your shoes!" "Make sure to wear sunscreen."
You can't "make certain" to do those things, since they are recommendations. It isn't you MUST wear sunscreen, or MUST visit New York City. Make certain is a yes/no, with a possible consequence if not done.