I'm thinking about taking my Faema Due A1 to a local market. At 220v 20amp, something like a 4000w+ generator looks like it would be needed...

Hopefully I just got some advice from a very-very safe thinking electrician, because those are huge and unwieldy.

4000+ sounds about right, given the power supply requirement you cite. As a rule of thumb, a genny shouldn't be operated at max. power for more than about a half-hour. The only time an espresso machine will pull full power is when it's warming up from a cold start. You need to know how long this takes; chances are a half-hour is plenty of time. Once it warms up, the heater switches on and off as needed; even in a busy cafe, they are not heating all the time. So, you could size for peak load at 220 * 20 = 4400-Watts. But, you may have some lights, grinders and a few other things to run. You need to take stock of these two and size to accommodate everything. Another thing you need to consider is whether you'll have any inductive loads of any consequence (motors and such), as opposed to resistive (lights, heaters and such). Generators are actually rated in VA (Volt-Amps), not Watts. For resistance loads these two terms are equivalent. But if you have and heavy inductive loads you have to take into account what's called 'power factor', which will require upsizing the genny a bit.
Edit: PS you also need to watch out, especially for Chinese gennys, if the rating is continuous or peak.

I think most generators less than 5KW are 120VAC. 5KW units have the two split phases for 240VAC. If I had a unit that pulled 4400W, I would surely get a generator that could source 5KW or more.

If you want silent operation and you can find used or order new an LPG gas lever machine that is the way to go. Ideally a 2 group but if your workflow is good you can accomplish a lot.

Astoria makes one that does both electric and gas so you can set it up at work or home on electric, then gas on the go.

As for feeding the water they are usually Dipper machines so they don't need a rotary pump or anything like that just a tank up high or a flowjet down low which could run off a small battery or tiny generator. You could even use a hand pump.