I don't think your first thing is a bug so much as it is an incompatibility. In this case you might be able to fix it yourself by (probably temporarily) loading the equip requirement plugin before my dual wield plugin. Without looking into it just yet, I suspect the incompatibility comes from the fact that I had to overwrite how the equip menu determines what items can be equipped in the offhand slot. In theory, if you load the equip requirement plugin first, it might resolve that issue, although it might cause more problems.
For your second issue, the plugin already allows dual wield actors to put shields in their offhand slot, there is no need to give them a second shield slot, as their offhand slot is supposed to allow them to put a shield in there, as long as your shields are etypeId 2 (the second slot on the types page in your database under equipment), and the actor (or class, or whatever) has the trait to equip some kind of armor that is this equipment type.
(I was gonna put an image here, but uploads don't seem to be working?)
If this isn't the case for your project, it's probable that the equip requirements plugin is also interfering with that as well, due to the aforementioned incompatibility. I will see if I can remedy this problem.
Edit:
You mentioned it had this problem specifically when you optimize from a class change, yes? Does that mean that the equip scene successfully prevents actors from equipping weapons they shouldn't be able to use? What if you optimize from that scene instead of via class change? Are you using my optimize equips on class change plugin for that?
edit: (didn't realize which plugin thread I was replying to, of course you're using the optimize plugin XD)