There are different diameters of Bullhorn bars--smaller ones for mtn bike gear I think, you won't get gripshift on them but you will fit mtn bike shifters just fine. I like bars with bar ends much better than bull horns because of the long rounded corner on bullhorns when riding the flat position makes my little fingers go to sleep.

I have been riding bulls and flat bars with barends since 87 and I have a new favorite bar end.-- https://www.ebay.com/itm/331951072972

With Adjustable height stem on both my swift and Dahon it is not an issue changing hand height on a ride especially when fighting a nasty headwind.

I would stick with Mountain bike gear. Most Road bike brake levers don't work with V-brakes.

Gearing is an issue if you cannot get by with a single up front and an 11/34 in back. I love the simplicity of the single up front on my folders. The new 11 speed GX 11/42 works well but the derailler is going to be close to the ground with 20" wheels.

The complexity of adding dual drive to an old bike does not sound like fun to me.

The MU frame from Dahon is about 1.6 pounds lighter than the Speed frame. I think the Speed frame folds a little better for putting into a suitcase.

Enjoy your new project.. Simple is my go to.