Connecting to Executone phone system?

I would like to set up an Asterisk box that interfaces with my buildings Executone phone system that is currently in the building.

The building manager has an interest in migrating to a VOIP system but doesn’t really know where to start. Neither do I really.

Currently I know that both the phone lines and the internet are provided by some crazy highspeed broadband from TimeWarner. This is not Road Runner but some business class connection that is the equivelent to Dual T3.

I would like to start testing an Asterisk box for Voicemail management and other basic features for now.

Qestion #1
Can i connect the Asterisk box to the Executone system as if the Asterisk box were simulating an Executone Phone?

Converting my lines to analog is an option but means I will give up the curent limetless line pool I have.

Question #2
I would like to be able to connect to the in office phone system from anywhere that I have my laptop online. I have heard this is possible but have no idea what I would need to do to get started other than I need a Softphone. But how does the system find me in some Coffee shop on a wireless conection in BFE Anywhereville?