It's funny, because a group of guys I was with recently had this discussion. It reminded me of this thread and discussion.
In response to your first question, when one Grand Lodge recognizes another, it also recognizes the Grand Lodges that the second Grand Lodge recognizes. Otherwise, it must state that the second Grand Lodge recognizes "clandestine Masons", which causes it to be a "clandestine Lodge". Thus, when the Grand Lodge of Texas recognized the Prince Hall Grand Lodge of Texas, it, for all intents and purposes, recognized those Grand Lodges which are in fraternal concord with the Prince Hall Grand Lodge of Texas. The exception comes from an old rule passed by the UGLE that says that, once a Grand Lodge is recognized for a territorial jurisdiction, no other Grand Lodge can be recognized for the same jurisdiction without the recognition of the first Grand Lodge. In simpler terms, the UGLE recognized the Grand Lodge of Texas around 1837, when it was formally created (if I'm remembering my chronology correctly). Several years later, the Prince Hall Grand Lodge of Texas was formed and established, but the UGLE could not recognize it due to this rule. However, when the Grand Lodge of Texas recognized the regularity of the Prince Hall Grand Lodge, it became eligible for recognition by UGLE. However, since Texas does not have visitation rights with Prince Hall Lodges in Texas, going to a Lodge which is only recognized by the Prince Hall Grand Lodge of Texas (and not another Grand Lodge in fraternal concordance with the Grand Lodge of Texas), visitation is prohibited.
So, to your comments about Illinois, here you go: the Grand Lodge of Illinois has fraternal recognition and visitation with the Grand Lodge of Texas and the Prince Hall Grand Lodge of Illinois. Thus, if I went to a meeting of the Grand Lodge of Illinois and there were members of the Prince Hall Grand Lodge of Illinois also in that tiled session, I am 100% allowed to stay. In fact, had the Grand Master of Alabama realized this, he would have realized that he did not have to leave the meeting of the Grand Lodge of Arizona at which he was in attendance.
Also, this means that, if I am in a Lodge under the Grand Lodge of California and also visiting is a member of a Lodge under the jurisdiction of the Prince Hall Grand Lodge of Texas, I am 100% allowed to stay.
This came up in the discussion we were having as we were reminded that we should follow the rules of the Grand Lodge under whose jurisdiction we are at that point.
TU