I hiked in the Theth area last year, in July.
1. GAS
Gas was very easy to find in Tirana, but only the type without fitting. You can buy a stove that fits these tubes. Both the stove and the gas tubes are shown on this photo:
http://karpaterna.se/balkan/albanien/02b.jpg
You can buy both stove and gas in many shops, even in small kiosks or (as in the photo) on the streets... The stove is quite large but doesnt weigh much.
2. WATER
We hiked Theth - Okol - straight north into Montenegro. Just north of Okol there was one source. And near a sheppereds house near the border was another. Otherwise we didnt pass any sources. If I would hike here again I would carry a LOT of water, at least in the alpine area. It can be baking hot as well, in July.
Down in the valleys you can use water from the streams (perhaps a good idea to purify it before drinking). But the alpine areas were very dry.
3. RAIN
It doesn't rain often in July, but it's of course possible... A simple poncho takes very little space and weight, so I would recommend that.
4. DAYS
Four days sounds good. You won't need to hurry then.
FINALLY
Just want to say that you will have a very nice hike! The Theth valley is amazing. I can recommend the Grunas waterfall.
Good luck!
Mats (Sweden)
www.karpaterna.se