help to get started with WordPress

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I’m very new to WordPress i am in school to be a Web Designer and i thought what better way then to use WordPress Blog to do some designing and much more. Well right now i have questions that i haven’t seen around here or may be around but are out dated so here are my questions.

1. Do you need to have a paid domain to be able to use the downloadable themes for WordPress? For example i wanted to use a downloadable theme but when i installed FTP it told me i couldn’t connect to my server which is ifollowyoux.wordpress.com, so does that have something to do with it?

2. Is there a difference between the free blog on WordPress then someone paying to self host their own blog?

3. If i were to buy a theme somewhere else for WordPress should it work for WordPress Blog? I am confused as to what is WordPress Blog and www.remarpro.com it is very frustrating i hope someone can enlighten me on that.

Basically what i want to know is do you need to have a paid domain to use all available downloadable layouts for WordPress Blog, and to do more things, to me it seems like it because i tried the videos about installing a theme but it never works because it says it can’t connect to ftp server.

If anyone wants to be a mentor, friend, or a guidance help for me can you let me know how i can contact you in anyway so i can get my website off the ground and enjoy my time here, thank you in advance.