It depends on the age of the woman. This holding the door thing is expected by some and apparently an insult to others. I hold the door for another men in case of a tie. If a woman is annoyed with you opening the door that’s a good early sign of trouble. You have been warned.
Picking up the first check. Why not leave it up to the man. Ladies make it easy on yourself smile and say thank you and leave it at that. Probably the number qualification of man is that he is at minimally secure. You don’t need to insult him try to pull rank and pay the check. Men if she is fighting over the check she will be fighting you about other BS issues. You have been ⚠️.
Dating should be fun. You don’t have to perfect neither does she. Take it easy on getting sex. Let a friendship develop first. A lot of very long marriage started with one person making more effort than the other until she finally said yes. And visa versa.