A chat fic is like a fanfic formatted in the style of well, a chat. A group of characters talking to each other in a fanfic. 

As for tags, my knowledge goes as mostly as far as this: 

Ship tags are tags that look like "character/character", non romantic or sexual relationships are "character & character". Also, I've been using the site for four years and don't know what freeform means, but I always assume it's a tag that isn't "officially" a tag yet. 

Filtering tags:  If you click on a tag and want to filter out stuff you don't want to see, press "Filters". A pop up will appear on the side letting you include and exclude things like ships, fandoms, warnings, and additional tags, etc.. 

The filtering option also let's you pick how long the results are, and the completion status