1) Keep MMR up until a "mid level" rating, and then get rid of it. - Reasoning - This will afford new players who are trying to get into pvp better "learning" match ups at the very beginning, but allow for a mix once they've had a chance to "learn the ropes". As it is now, players who actually enjoy BG's have a much worse experience because they are often faced off against the same opponents, over and over again, forced into meta builds to compete, and/or experiencing very long wait times. The player base just isn't big enough for a good MMR experience. Let the players mix.
2) Separate pre-made ques and solo ques : Do this in the following manner:
2a) Create a separate leaderboard for pre-made groups. Offer better rewards for groups, both weekly and per match. Offer much better rewards for the top 10 groups weekly. Consider unique rewards only obtainable from group pvp. Higher rewards should offset the increased wait time and encourage group participation. Reasoning: the same logic you use in PvE rewards in regards to dungeons and trials is also applicable to solving this problem in pvp.
2b) For the que have only two options - alone, or with a group of 4. Do not allow teams to fight with less than four (at least for the beginning). Only solo or with 3 friends.- Reasoning : group play is social. If you want to compete in a group you need to make friends. Even teams of two when the total per team is 4, can greatly effect the enjoyment of others in the match. Yes, this does put people who enjoy fighting as partners in the situation of finding more friends if they want to do BG's together, but this is necessary to maintain match fairness. 3 separate ques (one for groups, one solo, one for doubles) would likely greatly increase wait times. The reasoning for not allowing people to que with less than 4 is that it will reduce the amount of players who que in partners or teams of three expecting to get a group fill, but will not, thereby creating a worse experience for both them and their opponents.