I want a typography logo for an application. If I use free fonts for that, can I just use them directly without mentioning the creator of the free font, or without linking the page where I download them? Or do I have to?
Each font should have a licence that tells you exactly what you can or cannot do without it. Some require that you give them attribution, some require that you buy a licence if it's going to be used for commercial work. If you are unsure about the licence, contact the author of the font.
Spiral is right, you have to read the licence in order to see how you can use the font for free. I'm also a logo designer and when I need a free font for some commercial work I like to use http://www.fontsquirrel.com/ - a great collection of free fonts that can be used for commercial purposes.