THEMA: Best time of the year to start hiking?
Best time for hiking in Scandinavia is August til beginning of September - which of course would not work for a thru-hike. But I wouldn't recommend a thru-hike anyway on the E1 in Scandinavia, you should better make it within 2 or 3 summers.
So my advice: unless you're not a very experienced hiker, don't start before July. You might make it from Nordkapp til Grövelsjön from start of July until mid-September. For the rest of the Scandinavian section, you should wait for the following year and start again mid-June in Grövelsjön.