I have a few suggestions regarding both glue and edge finishing. The glue I like to use for lining materials, but suede in particular, is Eco Weld contact cement.
It's a water based glue, so it's thin, very easy to apply and ready to put together in minutes. Because of how thin it is, it penetrates the fibers of the liner giving a very secure bond, without the need of pressing it too much.
With the edges I normally do one of two things with suede. I either cut the suede at an angle, and finish the veg tan edge on its own. The other way is to cut the suede straight with the veg tan as normal, but to finish the edge wih edge kote.
As long as there's no grease or waxes on the edge of the suede, it will stick to it. There will be a tiny ridge from the suede though, because it won't burnish. But I think it looks nice, and usually go with option no. 2.
I hope this helps!
Alex