Your first issue has one simple major cause - you're not constantly detecting the linedef in front of you, just the fact that there's a wall. You hit it when you glide, it's set to your last touched linedef, and then you enter climbing mode. This is something I've wanted to change but never really had the patience to re-engineer, since there's no easy way to constantly detect the linedef in front of you.
The vertical movement thing is much simpler, on the other hand. FOF sides intentionally use the y offsets of their in-map linedefs unless you use transfer line, because the original Doom Legacy designers thought this combination of parameters was more appropriate for DooM mapping. You can work around this by making sure there are no upper or lower textures visible for the same linedef and then applying the vertical scroll effect to the in-map linedef.