1a is good.
1b is acceptable but not as good.
1c means something else. Grammar acceptable, but wrong meaning.
The meaning of 1a, is based on this saying: "I have more strength/skill/class/character/integrity/kindness/talent/goodness/etc in my little finger than you have in your whole body." ... Obviously it sounds strange to say "more brains" in this kind of sentence, because the brain is not located anywhere except in the head, but when you know this style of sentence, you can understand its meaning. "Brains" here, means "brain power" (intelligence, knowledge, etc). "Little finger" means "pinky finger" (the smallest finger on a person's hand).
2a & 2b are both correct and have the same meaning, but 2a is a more educated & classy way of speaking, while 2b is a lower class way of speaking, but still technically valid.
3e is wrong grammar, and can be tweaked to make it technically valid but it would still be terribly inefficient & convoluted - there are much simpler & clearer ways to say the same thing. All the other options in section 3, are technically valid sentences, but have varying meanings and varying levels of clarity. 3a is a slightly old-fashioned way of speaking, and to increase clarity in the modern day, I would personally say it like this: She always acts in the way that appears best to her. Or, to sound a bit more sophisticated and to remove any doubt about the meaning, when speaking to a well-educated native speaker: She always behaves in such a way that she deems to portray herself in the best light.