Zesty, forcing you a background sucks a bit.
dragons can take character levels, all monsters can take char levels as far as i can tell, some won't make sense (no 20 lvl wizard squirrels) but it's doable. Bahamut has a keckton of non dragon levels and a dragon of the great game literally has great powers that do things, the entry is purposefully vague on how far they can go, just that they trade innate spell like abilities (which normal dragons do have) for more physical strength.
I would say that you are a half dragon, but since you've been playing as a human then you'd be an exceptionally weak half dragon with underdeveloped claws and flame sac, virtually indifferent from a human.
As for the paralysis, spells can specifically mention that they effect creatures that are normally otherwise immune, it could be homebrew i guess, no real answer unless you knowledge arcana on it while it's being cast. They way i like to justify spells like that would be that it's a mind compulsion effect that makes you think that you can't move anymore ie you forget that you can move and just stand around like an idiot. But that should come with a will save.
Using that much homebrew is kinda a dickish move.
As for daddy's death. He was obviously hit by a critical sneak attack with so much bonus damage, that it became a massive blow that he failed the fort save on.
NPC-NPC intercation can be preplanned and don't require rolls. Also the DM doesn't have to let players see rolls, hence the dm screen and several rolls are supposed to be done in secret too.
I do agree with you that they DM has communication issues, so you should have talks with him that are civil and calm. Be prepared, and do it when he is free. If he can't communicate, you being a bad communicator just makes it worse. Also, rules discussions should be left outside the game, at the table, the DM has to improvise and keeping the game moving takes priority over wasting time on the process of ride checks. If there is someone that the DM takes criticism well from, then the DM prolly has trust in that person's experience, and any corrections that you may have, you should prolly try to channel through that person.