So how about that, front wheel flew off!

Yes the wheels do have a bevel.

Should I buy different lug nuts? If so from who? How can I find length of the lug nut?

Are your current lugs .750" reach? How thick is the wheel hub, 1"?

then maybe similar to these lugs.......
http://www.ezaccessory.com/Cragar_Mag_Extended_Style_Lug_Nut_1_2_20_p/8804.htm

and heavier washers..............
http://www.ezaccessory.com/Cragar_Center_Washer_p/779.htm