Magento and HTTP/2 : what is the current status?

There is no problem with HTTP/2 "just working". But there is opportunity for further optimization.

My understanding is it is worth looking into capabilities of your CDN provider if you want to take full advantage of the push support. E.g. when request for first CSS etc file comes in, server can start pushing other files it knows you are almost certainly going to need. At least one CDN you could tell it the extra files to push. This is a part of what means you don't need to merge CSS and JS files - using pushes can be more efficient than sending a big merged file. But to get maximal performance, the CDN needs to know "when you fetch X, then push Y and Z as well". I don't know if they magically work this out for you or not (based on past traffic patterns).

You definitely can use Http/2 with any version of Magento. And yes, you need to enable https for all pages (it's recommended setup for M2, why do you not did it before). Also, bundling of js files don't make sense with http2, so better to disable it

If you want to set all pages to HTTPS, you might also want to enable HSTS (More info: https://en.wikipedia.org/wiki/HTTP_Strict_Transport_Security).

For the rest of it, I never had any trouble using a webshop on HTTPS/2, so like Alan and KAndy say, it should just work.