Eventually the roots of a Zelkova will penetrate the area beneath the patio. I'm not sure I'm accurately understanding the patio's construction: dug down then an additional 3 feet above grade? In any case, you've created an ideal environment for roots of any sort of tree - relatively loose and moist. If you plant only 10 feet away, a fast growing tree like Zelkova will have its roots beneath the patio pretty quickly. How much damage they will do and how quickly is impossible to predict. Your dilemma is pretty common for west facing patios and decks. You need the shade from a fast growing tree, but you want to avoid root intrusion. The truth is you really can't have the first without the risk of the second. Artificial shade may not be as attractive as a tree, but would have the virtue of eliminating any root damage danger. You could also consider planting a tree such as a Japanese maple with a compact fibrous root system. It would be a long wait for any significant shade, but would not destroy the patio. As for the forsythia, they're easy to move, but spousal horticultural disputes are best avoided by all third parties.

A lot of shrubs send up suckers from the roots. These suckers live for X years, with the idea that long before that one gets old and dies off the shrub will send up a bunch more. The idea behind normal, rejuvenation shrub pruning is to cut out all of the older suckers, and leaving behind the younger ones and room for new growth. So while the entire thing can be quite long lived, individual suckers, canes, branches - whatever you want to call them - generally have a shorter life span. Since this forsythia has been trained to a tree, it only has one of these. When it gets old, the whole thing will be in trouble. The question is how long might that be, and I haven't been growing mine long enough to know. It still has most of the growth it originally came with.

none that I am aware of. The leaf is a very unique shape that I dont remember seeing before anywhere.

Of the two this is cherry