fathom - 9:42 am on Jun 23, 2003 (gmt 0)

Is it valid to change H1 apperance with css styles or just with <font>?

The use of CSS is a valid way to define prominent page info - such as a page title. The CSS provides flexibility.

Is it valid to put text links inside <h1> tags?

Yes - The first Page Title, a sub title H2, the third title H3 etc. You should always have normal body text between each H tag use though.

Is there any way to check if your site is banned from google or other search engine?

Search for it, if it was there before and not now the possibility does exist.

However using H1 elements will not get your site "banned" unless the possibility exists that everything in your is defined as H1.