Now that my memoir is published, I notice how there are multiple chapters beginning sharing the same page that the previous chapter ended on. I don't like how it looks at all. Looking at other author's published books I notice that their book's are not the same way as mine, with multiple chapters sharing pages. Should multiple chapters be sharing the same pages?!
In MS Word, Ctrl+Enter inserts a page break (moves on to a new page). There are also options in the 'Layout' tab for various types of section break, although I'm not fully sure what advantage these would have over normal page breaks (unless you're using the 'start on next odd-numbered page for example).
As per @F1Krazy's comment, whether or not you like MS word is purely a matter of opinion, but I know Google Docs offers similar features and there is a libreOffice alternative too (although I've never tried it). Try them and go with what you prefer.
Whether or not chapters should share a page is also somewhat case-specific. By 'multiple chapters' I assume you mean no more than two - I've only ever seen a chapter shorter than a page in one book before, and there it had a (very empty looking) page to itself (it was mainly as a joke, the chapter was called 'The Hunt for [Character]' and the only sentence was "Oh no wait there he is, didn't see him there for a minute."). Actually make that two books, because I know there are plenty of examples of multiple-chapter pages all through the Bible. Apart from those examples, I've seen some books where a chapter starts on the same page as a previous chapter ends, but it's not as common as just giving each chapter a new page to start on. Where it does happen tends to be (from memory) where the previous chapter finishes on a cliffhanger or similar so the narrative flows smoothly into the next chapter (rather than a break in time, place etc across the chapters). Moreover, those books also tend to use section breaks every few chapters which are much more defined, to break up the text a bit - structurally I certainly wouldn't advocate running the chapters together in this way all through a book. Have you asked the publisher about it?