Happy Cow lists a number of organic/health food stores in Haifa, but the websites I found were all in Hebrew with no English option. Don't know if you speak/read Hebrew or has someone around who does, but that might give you an idea of what's available.
The last time I was in Israel was when I was 13 and not vegan, so I never paid attention to this stuff. (Not to mention, that was over three decades ago and the landscape has likely changed since then.) But I do remember that Israeli food was very very veg friendly. (My sister was vegetarian at the time.) Lots of incredibly fresh fruit and veg, lots of legumes. I think that even if you don't find specialty items like nooch and gluten, you can eat there really well on what is available. Plus, amazing falafel everywhere you go!
(Nooch tip: if you find out what to look for, check the nutritional supplement aisles and not just the food aisles. That's where they hide it here, so I wouldn't be surprised if it's hidden there too.)
ETA: Just googled "nutritional yeast Israel" and found out that it's put out there by a company called "Tvuot" and that it should be available at the Eden Teva Market
which has a store in Haifa. That might be your best bet for finding the other stuff on your list too.