Does buying the RPG marker give you the download or a disc?

When purchasing any RPG maker, does it come as a payed download for the computer or does it get mailed to you by a disc? I'm asking this because the purchased asked for my address and phone number.

Email with download link.

You get a download link with an email, but if you sign up to rpgmakerweb home page (different from the forum) you'll have access to the product code on "your account", so if you switch computers you can still use the same product code and there is even a download link in the same section to redownload everything you ever purchased on this site. I think the steam verison does something similar but I don't know for certain.

Yes you still have to fill in a home address and I think a phone number but nothing gets sent to your home address with the online-only products.

Do you need to type in the product key every time the program is opened?

No, just the first time.

EDIT: Oh wait, it worked this time.

that is because you have not yet activated and are still in trial mode. And that will not change as long as you click on "continue" (continue the trial that is).
You need to click on activate and complete the activation once (which will require an internet connection) and then the screen will never happen again.

If you get an error message during activation tell us which one and we might be able to tell you where your problem is.
It could be that your registry is damaged, that the internet settings block contact to the activation server or a few other things, but activation has to be completed to make this screen vanish.