I'd be friendly casual, by the sound of it. If you pick her up and walk to the car with passenger side closest, maybe open the door for her with a minor goofy flourish. See if she laughs a bit - it's good to break initial awkwardness. It's also ok to admit that you weren't sure about the etiquette (this is not because it's your first third date, but because everyone is different). She'll probably tell you it's fine without, or that it's cute, etc. try to listen to how people want to be treated. If date is goes well, you can offer to walk her to the door - I recommend being verbal and brave but not pushy for everything after that.

As for clothes, it all depends, but look in a full length mirror and make sure you're wearing something that helps you feel confident in the setting.

For after-date texting, your call. It depends a lot on your baseline texting relationship and if you even liked it enough to want to date her again!

There's a lot of mythos about third dates, but you can navigate how much weight it has - some relationships move slower, some move faster. Being honest without overbearing is generally the best approach.

GLHF!