link farm - I do not think this means what you think this means

The 100 link thing is a bit out of date - here and here - but it's good that it makes you stop and think about what you're doing.

As dignan99 said you need to think about your internal link structure. There are a few pages on SEOmoz that should help - 1 2 3 - indeed you should be very able to work out what to do from those.

Basically having a whole bunch of links isn't a huge problem, but there may be a better way if you sit down and think about it

It depends. What's written into the agreement?

If they've built links on other people's sites then it will probably be too much of a hassle to contact all of them and ask them to remove it, so it will either naturally run out (if it's paid and you're not given the contact details) or remain there for the rest of it's natural life.

Alternatively if they run the sites they've been building links on (and it is the easiest way to guarantee clients will get links on sites) then they may remove them to make way for new clients links. I've certainly seen this happen.

It's important to note that Google doesn't overly care how quickly you get links, but it will certainly notice if you lose a lot quickly! Aa it means you've either bought them and they've expired or something has happened to make people lose trust in your site, either way it's going to raise some flags and possibly have someone look a little bit closer into your link profile.

Double check what's been agreed, find out who owns the sites the links have been built on and speak with the agency before you do it. If they're reputable I doubt they'll try and screw you over.