Solo crossing Vonarskard to the south on foot

Hello all,
I am planning to cross Iceland solo on foot next summer. Some questions arise:
1 - Is it possible to cross the Vonarskard from north to south, coming from Nyidalur hut, between the Koldukvislarjokull and lake Hagongulon, crossing the Kaldakvisl river and the Svedja river?
2 - If not, what is the best alternative? Cross the Kaldakvisl river to the east, go south on the Koldukvislarjokull glacier and cross the Svedja river further south, OR go around the west side of lake Hagongulon, cross the Kaldakvisl river on the south side of the lake by the dam and move further south?
3 - Is it possible to cross the Tungnaa south of Jokulheimar hut?