I noticed that as well, but some people prefer to use their left hand for drinking, so their right hand stays warm for handshakes.
As for your questions, i was stumped on these ideas for a while before i posted my deduction. Who sent the letter to Heiji. It wouldn't be the Mistress because she made the crazy diamond illusion, and fiercely withheld info. The secretary was way to unco-operative and secretive. Shiina would have brought more cake, and Fujinami shouldn't have known of the dying message. Therefore the maid had to do it. The one who sent the letter is probably the culprit, based on how it was written. It seemed like a test to see if she could pull it off. This means the maid sent it.This person would naturally give them leads to discover the trick, and even if they did she would cover it up by killing off the mistress to make it seem as a suicide. Why did she do this, because she is a distorted existence, thoughtlessly conjoured up by humans. Did she know they were going to visit that night, probably found out right after the Mistress told her, and that's why she started making mistakes. She sprinkled the poison on the doorknob to elude herself from suspicion. This camouflaged her and made it seem as if the Mistress did this. The problem was Heiji brought friends that unveiled her trick. She already was going to use Jastrow illusion, but since Heiji was coming so soon, she had to do something. For your last question, All suspicion was on her, so she had to say something, and help them see her fake set up, this is why she dropped the poison capsule in the mistresses drink. For the dictionary in the PC room, i figure The mistress hid something there and it was replaced with poison. At the end Conan noticed the maid didn't drink her tea with everyone.
I think i answered your questions :grin: