Reporting comments

Is reporting comments solely for spam or can I report comments if they are links to shady websites, inappropriate or don't have any connection to the thread?

Shady? If it's illegal then no, if the comment is OBVIOUSLY an ad then no, otherwise you have to depend on the spam rule. Here's the relevant FAQ section (emphasis mine):
Q: What can't I post on the forum?
A: On the forum you cannot publish the content that:
- violates the law,
- propagates fascism or any other totalitarian system
- incites to hatred (on national, ethnic, racial or religious grounds),
- shows pornography,
- is insulting or offensive,
- advertise other portals or entities (without the approval of the administrator of the site).

As for the rules about spam, it's not in the FAQ, but inside a comment made by a moderator way back, near the end of the first page of this thread:
https://gamehag.com/forum/t/58039-penalitiesxp-taken-away-bans-and-more
Spam on Gamehag (or any public forum) is generally defined as repeated, unwanted, and/or unsolicited actions, whether automated or manual, that negatively affect Gamehag's (or any public forum's) users, communities, and/or Gamehag itself.
So "inappropriate or don't have any connection" links would be considered unwanted actions that negatively affect Gamehag's users and can be reported. Whether they will be acted on or not depends on the view of the moderators, however.