Sharapova the toughest mentally?!
I know this is not something many will agree with, but I do believe Maria is the best mentally. She wins SO many matches, against the best and lesser players, by simply keeping calm and believing in herself. She takes it one point at a time, which means she doesn't allow bad feeling or nerves to take over for a whole set of points. Her opponents will generally always falter mentally before she does, as they don't have her mental stamina or fortitude.
Sure, her record against Azarenka and Serena has been poor this year, but I feel it's more down to them being bad match-ups for her rather than any mental fraility. The only match where she slightly lost it mentally was at the end of the US SF, but apart from that, she's lost to them due to their ability at exploiting her weaknesses better than anyone else, not due to lack of belief or mental issues.
OP and Griffin both made great lists, I'd like to add few things.
1. I don't think that Serena lets opponents get inside her head, my impression is that sometimes some bad misses get inside her head (rather than opponents) which was mostly visible in the first part of the season when she simply couldn't win ugly.
2. I don't think that Sharapova is the strongest mentally, Vika and Serena are stronger mentally.
3. Errani's return and mental fortitude are seriously underrated. I'd like to add it to list of her strengths.
4. Azarenka has a great touch, good volleys and drop shots.
I somewhat agree with number 1, although I do believe opponents can get inside her head. Razzano was a prime example. She kept the pressure up against Serena the entire match, and didn't falter. When Serena made that fatal decision to stop the point when she was winning the tiebreak, she completely crumpled and Razzano took full advantage. People forget how badly Serena imploded in that match due to the final game.
It's a combination of putting too much pressure on herself and opponents getting inside her head in the end. Zheng did a fantastic job of that at Wimbledon, she won a huge majority of the rallies cos Serena's ground-game was so off she couldn't handle Zheng's early flat hitting and led to her freezing whenever she had any opportunity. Only her serve saved her that day. The US final also showed how when it's not going well for Serena that she spends so much time having to keep calm that it can have a real negative impact on her play, cos she loses focus and rhythm.
It's making her feel uncomfortable though that is the hard bit, that's why it's so shocking when Serena does fray, cos most of the time she's so in control of her matches there is nothing for her to get stressed about.
BTW, I agree with your point about Azarenka, she does have great touch, I think she should move forward more, she's more than capable. She has excellent court-sense as well, and it's an area of her game that she doesn't get enough praise about.