Tasks after competition

It would be nice if solved tasks on competition are automatically solved on tasks added on training page

Hm, I don't think so. I think now is perfect. Maybe someone doesn't want to share his/her solution with the others, so there is no way to see it if you are not admin or if he/she doesn't submit it. However, this is very individual :)

Yes, it would be, but only if there is a possibillity to re-submit your code so that newly submited code is visible as your source code.

If you submit some faster, better code and it gets accepted after the contest ends, and your contest code stays as your source code for that task... It's not desirable...