Binny,
I'm a big fan of alcohol stoves, too. I've built both the pop-can type and the Cat Stove, and I'm actually a bigger fan of the Cat Stove (Google it if you're not familiar -- it uses two cat food cans and tends to work a little faster than the pop-can kind). Yankale is right that gas stoves are the best traditional option. But alcohol stoves are great for the INT and I'm glad you asked these questions.
1) Yes, you can carry these stoves on planes. On our first INT hike, we built an alcohol stove brand-new for the trail, just so that on the flight to Israel, there wouldn't be any issues with fuel residues, etc. The stove was no problem when we went through security. Our idea was that the stove only cost about two dollars to build, so we could throw it away before getting on the return flight to the States. But we decided to try taking it on the plane, anyway, and again, it wasn't a problem, even though it had been extensively used on the trail. On last spring's INT hike, we brought that same old stove, as well as another one that had been used. Again, it wasn't an issue at all.
2) Yes, you can find fuel in Israel. Of course, the ease/difficulty of fuel resupply depends on where you're hiking, but the best place to get fuel is actually at a pharmacy. Israeli pharmacies carry alcohol for medicinal purposes. You can usually find "70%" alcohol, which means it's only 70% pure. You can find various percentages all the way up to 95%, I believe, but that's a bit more expensive. I was skeptical that the 70% alcohol, which actually is mixed with some water, would burn hot enough to cook our food. But it actually worked really well -- about as well as the HEET you buy here in the States.
So anywhere you can find a pharmacy (just about any town), you can find fuel.
Warning, though: The alcohol you can buy at the pharmacy is drinkable. But that doesn't mean you should drink it. It's almost-pure, and therefore completely different even from taking a shot of hard liquor. Especially out in the wild where you need to be careful, anyway, just don't do it. Likewise, you might get some funny looks from the pharmacist unless you explain why you're buying the alcohol. Usually, once we told pharmacists that our stove used alcohol as fuel, they only had to look at our suntans and our faded clothes to understand that we were "shvilistim" on the trail.
If you've burned HEET in an alcohol stove, then you're familiar with about how much fuel you need. The size of the alcohol bottles you can find will depend on what the pharmacy has in stock. Sometimes you can buy a few 200-ml bottles, and occasionally you might find a 500-ml bottle. It all depends. But as you know, just a little bit goes a long way.
You'll find that an added benefit of your alcohol stove will be that INT hikers will be amazed by your silent, reliable little gadget. A lot of people asked us where they could find plans for the Cat Stove and planned to build them themselves. And the guy who helped me get started on the INT used an alcohol stove as well.
But I echo Yankale -- don't plan on having any wood fires. You might get lucky and end up camping with some people who brought their own wood, but otherwise, always plan on buying and carrying enough fuel to get you to the next town.