Let me see if I hear you right...
You have two LANs, with a group of computers (possibly other devices) on each. Now, you want them to communicate ?
Are they at the same location ? How much space do you have ? Etc...
I can imagine you have a few options:
1. You could combine them into one (you didn't give much info so I'm going to throw this idea out just in case it's possible). This may or may not be desirable.. depending on what you're trying to accomplish.
2. Use a device that links them together... But again the best approach could depend on location of networks, etc.
3. Have them both connected to the Internet and go through that way.
Note that I'm quite out of the loop on setting up rather large networks, but, I think those are your options; there may be more though. If anyone else has any other ideas though, please do mention them, as I haven't done much related to this in a long while ...
Oh and to answer your questions:
1. You should be able after it's setup properly.
2. You'll probably use TCP/IP, yes.
3. You should be able to use SSH.
As for your last question... I personally perfer static ips, but for larger networks and especially those that don't require static ips you might be fine with dhcp...