You're going to need an electrician to tell you anything more, really. Even if the panel is a 200A rated panel, the entrance conductors might be only 2/0 or 1/0 AL. Either way, you'll need a permit, inspection, and meter pull (unless you have an outside disconnect) and it'll have to be done to code.
From what I can see, in your existing panel you'd likely be able to install a NEMA 14-50, or you'd be able to set up the HPWC with a 40A charging current only (as mknox said). Looking at the loads listed, I see a couple of breakers that have A/C noted on them (probably for small window units) plus the 240V A/C outlet you note, refrigerator, etc.
An electrician can look at what you have and tell you how easily (or not) you could upgrade things.
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Should probably merge this with the other thread by the OP:
http://www.teslamotorsclub.com/showthread.php/14709-What-Do-I-Need-To-Tell-The-Electrician-For-My-Electric-Meter