1) Missing face
When a framed wall connects to a wall below, the bottom face is not rendering:

Note that this is not observed when there are e.g. glass panes inside the wall:

2) Not connecting
The framed wall doesn't connect to visually full blocks, in this case Integrated Dynamics Facade blocks:

FramedBlocks-2.14.4.jar for Minecraft 1.16.5

Weird, I'll have to look into that, that should just work the same way the cobblestone wall works.
Please make a new issue for this with the relevant version details to make it easier to keep track of.

Almost the same except it's an AE2 facade that acts as a full block for vanilla cobblestone walls but not for Framed Wall:

#111

Regarding 2: You're correct, vanilla walls also don't connect. I'll report it on the ID github.

Thank you for the feedback, I'll close this as fixed.

1) Missing face

Nice catch, I completely missed that. The walls are a mysterium sometimes and I am always discovering new connection behaviors I didn't know existed.
I have pushed a fix for the incorrect face culling, will be released with the next update. As this is non-critical, I will not release this immediately.

2) Not connecting

In terms of the connection logic, the Framed Walls are equivalent to vanilla walls, so vanilla walls will most likely not connect to those blocks as well. Have you tested what happens with those special blocks and vanilla walls?