>>120210Do not expect to catch anything if you haven't tried it before.
>>septemberIt is possible. I was there in late september once. Just north of Abisko. It is the prettiest time of year, but some of the passes might be closed due to snow. When I was there we had anything between -10 to 15 degree C weather at around 900 m. I post some pics of how it looks like in September.
The best time to go would probably be late July and through August because there are fewer mosquitoes late in the summer. But more people though. You probably cannot go earlier than 15th of June, but it depends on the amount of snow.
>>carrying our own foodRemeber you can buy more foods in the small huts mentioned. It is more expensive than the supermarkets, but is a very good option for stocking up on oatmeal, pasta, rice and other heavy/bulky items. You can find a list of what is available somewhere on the interwebs. I will look for it later.
If you want me to comment on the route you have to provide a more detailed map. Those lines are so narrow. I would climb Kebnekaise as a day trip and hike with rucksacks the other days.