is it possible for mangas to start up again after a while like if they were incomplete or the ending was a cliff hanger?

Magic Kaito was paused 20 years ago because the manga started drawing another manga that is very popular now (Detective Conan). The characters from MK had guest appearance in DC and we're so popular that the mangaka decided to draw some new chapters during the years. And now, after 20 years MK has his own anime even though it is incomplete. We are waiting for the mangaka to finish the long running and boring manga about a detective, and continue drawing MK. That is, if he doesn't die in the meantime... I mean 20 years! -.-

The one that pops up in my head is Dead Man Wonderland. In the case the woman making it got pregnant and decided to take care of her business. In her case she'll most likely go back to it but it's hard to say in it will be a few months or a few years.

It's really on a case by case basis. When creators walk away for personal reasons it's 50/50. If it's an actual cancellation your only hope is merch sells skyrocket in reaction to the possibility that it will disappear from shelves

It just depends. Sometimes a manga will go on a hiatus. When this happens there's a chance that it will restart. If something gets flat out cancelled, then then that's usually the end of it.

possibly it usually stops because a publisher drops the artist but sometimes a different publisher takes them up or they write a new season

I think it depends on how popular the series itself is and if thd publisher is still doing it