Negative. Only a VFG (vertical fore grip) will get you in trouble if your rifle is less than 26" overall....which I'm sure yours will be.
No, not at all
I'm sorry, please disregard my previous answer. You are talking about a handgun, not an AR, but it is only a control item, I do not believe that it creates an SBR. I expect either possibly a fore grip and definitely a buttstock would constitute an SBR. I kind of doubt this would do that, but I'm not related to BATF or any other law enforcement. I've looked around on the web and all I can come up with is that an AR style pistol can always become an SBR or rifle, but not vice-versa.
If you're talking about adding this part alone to any AR-15, then no, that has no relationship to an SBR.
No, in over ten characters