Permanently Deleted
Yes. In the US, a gap of about 3/4 inch from a finished floor is normal. It acts as air return when the door is closed. I know in some other countries they put a hole in the wall above the door for this purpose, usually making it look decorative.
One of these door bars could help: https://a.co/d/h56YulW
Doesn’t really address the fundamental problem, but it’ll make getting the door open harder.
This post combined with your new post about not being allowed internet access in your bedroom hints at a different story than a narcissistic parent. The fact that you aren’t willing to use the computer in the public spaces in the house and want to sneak access back into your bedroom says your parents fear inappropriate use of the computer, whatever that may be. And if she comes in and is hanging out in your room, it’s not to annoy you, its because she’s scanning everything in the room for signs of stuff they think you shouldn’t be doing or shouldn’t have.
This isn’t to say you did something to provoke suspicion, some parents are really conservative and just suspect kids are up to trouble. But trying to get a better way to lock the door combined with trying to sneak internet into your room gives off alarm bells to parents.
If you can leave and find a place to live, it is better than living with a narcissist who doesn’t respect your privacy.
My parents also would barge into my bedroom whenever they liked, after a big argument, my dad respected my wishes, but no matter how many arguments about privacy we had, my mother never listened. I began to just be naked whenever I was in my room alone, and she stopped. When I wasn’t in my room, she would still enter, but I didn’t keep a diary and my computer was encrypted.
One important contextual item: how old are you?
Less important but still useful: what jurisdiction are you in? Is your father her enabler, absent, elsewhere?