Can servicepeople get their 20/30 years in by switching services, say from the Army to the Navy?
Yes
Yes, the branches are interchangeable for that and it can be fun for someone who wants to try different branches, for instance, a guy who does Navy stuff for a couple of years and then switches to the Army or Marines for something different, or the other way around.
The Reserves and Guard can be used for a change also, say an infantryman who joins the Navy Reserves when he leaves active duty.