Help, am I a normal cat owner?

I need to know if the way I love my cats so much is normal or am I reflecting some sort of dependance on them or something. Like, I would actually attack someone if they hurt my cat intentionally, I don't want people who can't handle cats being near my cats, I get very angry at my dogs when they chase my cats (I don't hit them or anything). I don't know if the level of protection I feel that my cats need is even normal anymore.

I get on full mental breakdowns by imagining something happening to my cats if they go to the street and they're not careful. I was constantly grieving a cat because a few have died with short periods of time between their passing and I got stuck in that feeling of sadness because they're gone, even with the ones that are still here.

I feel like my cats will die very soon and I need to treat them like the most precious babies ever because I don't want them to go thinking they weren't loved and that's given me serious amounts of anxiety. :(

Is it normal to feel like this? Am I reflecting some trauma on them?

If someone could give me their opinion or share their experience I would appreciate it. :(