Could someone please remind me all the words that are used for to know? I don't really remember any of them and how they are used.
When speaking of people that you know להכיר is used. It's also used for things that you recognize or are familiar with. לדעת is the stronger one - actually knowing something.
אני יודע שזה נכון
אני מכיר את המילה הזאת
First name = "שם פרטי" = private name. Last name = "שם משפחה" = family's name.
Family = משפחה
Last name =שם משפחה. This is because your last name is the name the whole family shares, so it's a family name
Yes, in this context it might be just a little bit odd... but still technically correct.