Yeah usually it's fine however different forums have different rules so best to check with each one first!
every forum has its own policy but in general, it is allowed to use your company name/url in the forum sig
it depends on the TOS of the forum provider in most business forums it's allowed but I also know a few where you are not allowed to use your signature for advertising your services.
wtf you have SEO in your screen name and don't know the answer to this question? something doesn't add up.