To get in excess of 7 speeds, you'll need to change to a freehub system with a 130 mm hub width. I've done this a couple of times on vintage steel frame bikes but not on a folder. The folding bike may be more of a challenge, due to shorter chain and seat stays. You'd want a shop to evaluate that.

What is the gear size range on your current freewheel? As mentioned above, it may be simple to change to a different freewheel. You can usually add a couple of teeth in the lower range without needing a new derailleur. Chain length may be an issue.