Unless the member of staff has a good understanding of up to date SEO techniques I'd be careful. I wouldn't look at it as building links, look at it as finding relevant websites that will help you drive traffic to your website. Industry specific websites that will help you drive the traffic you are looking for.

Some link building companies focus too much on the number of links being built rather than the quality and relevance of the links. I'd find a list of competitors and do a link audit on them and see if your links can go on the same sites.

page authority and domain authority are a good measure of how good a website is (but not the only measure!). Think about where your post and link are going to be in the long term. For example, if you are guest posting, the post may be on the home page for a week or 2 but then it will be archived so you need to look the inner pages of a website and look at the authority of that page.

If a website has a much higher page authority than domain authority then it's a sign to me that it isn't that good. It'd be much better to have a higher domain authority than page authority because it will show that the website has been up and running for a while.

Also look at the last time Google cached the website and the inner pages, that way you will see how often Google revisits the website and the chances of your link getting cached. Look at some popular websites and look at the domain vs page authority scores, the home page maybe slightly bigger but not that much.

Hope that helps!

Ok, you'll probably be able to get the good links for your new domain then. Good luck with it all.

The best thing would be to clean up the bad links, file a reconsideration request and then 301 the old domain to the new one...that is if you have some good links to the old domain. If you only have spammy links then starting afresh would probably be easier.

Whilst it is likely that the links had a negative effect, it seems unlikely that they would have had such a quick effect. Links via forums aren't the most "natural" of links so I wouldn't advise sticking to that. When you are building links, ask yourself "do the links look natural?" Make sure they fit in with the content of the website and make sure that the website you are linking from has some authority (look when the page was last cached) because if it takes Google months to visit the website then it will be months until your link is cached.