Regardless is a word in standard English. Irregardless is not.
Short version of the story: the less takes care of having to put ir in front of regardless.
Don’t say “irregardless.” Just say “regardless.”
(Apparently, irregardless is a word in some dialects, used to shut down a conversation. So unless you grew up with it as part of your culture, and you want to be rudely abrupt, don’t use it!)
This one’s easy. Your means it belongs to you. Your pen means the pen belongs to you.
You’re is a contraction combining the words you and are. So you’re means you are.
So we can never accurately say “Your cute” unless that person has something called a cute. We would want to say, “You’re cute,” which translates into “You are cute.”
If you can say ,“You are (whatever),” then feel free to combine you and are into you’re. Otherwise, if you can’t say “you are….” then you probably want your.
You have my permission to make every legal effort to change every sign or advertisement that gets this wrong.