Partially moving some emails addresses to 365 from existing domain but not all.

You can do a pilot with some of your users and email addresses, independent where your domain is hosted: https://support.office.com/en-us/article/domains-faq-1272bad0-4bd4-4796-8005-67d6fb3afc5a#bkmk_pilot

 

No hybrid required, if I understood your question correct.

Yes, this is called Hybrid setup. You can have e-mail boxes on-prem or on Office 365 at the same time. So you can move half your users over and not the other half. Or one department for awhile then the rest. It's really up to you. And you can even move the e-mail back to On-Premise if you want later on.

Here is the documentation for it all: https://technet.microsoft.com/library/jj200581(v=exchg.160).aspx