Is it possible to do these?

I've made 2 small games with Construct 2, nothing great or insane but I'd like to see what else I can do. I have an idea for a browser based game that I've wanted to do for a while now but I'm trying to find an engine that is capable of it. So I'd like to find out if Construct 2 can do the following:

• Connect to a MySQL Database?
• Use $_GET[] Functions to see if user is logged in on the website?
• Display PHP variables?
• Display MySQL Data on Textboxes?

I want the game to be open to anyone to play but also save data for registered users, nothing major, just things like a score, currency, username, avatar.

Yes, you can easily do all that - using AJAX to pass the info back and forth to php. There are several good tutorials on how to do it that helped me get started.

Oh sweet, I don't suppose you could point me in that direction?

Here's an excellent tutorial. I don't understand much of this stuff myself but it should give you a good starting point for what you want.