Flyback converter desing. Problems with requied gap and number of turns.

Hello,
At first, I am sorry, but i have to post all my calculations as images.
I have problem with requied gap for my core and number of turns on both sides. I don't know how to calculate primary inductance too.
I was trying to design flyback by using this website: http://schmidt-walter-schaltnetzteile.de/smps_e/spw_smps_e.html but i don't know how the autor gets the numbers of turns for both sides.

Core: ETD44
Ident. 1.5
Manufacturer:Siemens
Al/nH: 194
Ain/mm2: 17
lin/mm: 103
Amin/mm2: 172
Wmax/µWs: 6862
Bmax/mT: 281
N1: 5
N2: 6668
N1 - number of primary turns,
N2 - number of secondary turs,
Wire Data:
d1 ? 2.38 mm
A1 ? 4.45 mm2

d2 ? 0.08 mm
A2 ? 0 mm2
How to calculate wire diameters?

I also did calculations in Mathcad so i am posting my results as jpgs. I am stuck at required gap and all the next calculations goes wrong.
http://obrazki.elektroda.pl/4731388300_1444160177.jpg
http://obrazki.elektroda.pl/2866997200_1444160178.jpg
http://obrazki.elektroda.pl/5119057900_1444160180.jpg
http://obrazki.elektroda.pl/9450762900_1444160181.jpg