He is also proposing a "bad leaver" clause where founders have to sell all their vested or unvested shares at the lowest value between the nominal and subscription price.
NO, it's in no ways normal. In reading how you have framed the question, this investor sounds to be acting in bad faith and is also setting you up to fail by introducing terms that are not standard to how quality investors interact with their investee companies.
It is however very standard to have a first right of refusal to purchase your shares should you wish to sell. But that is not at all what you have stated.
Happy to talk through the particularities of your situation in a call