Tree paeonies are deciduous so yes they lose their leaves in Autumn.
Three weeks for the flowers is about right.
If you must prune then when the tree is dormant is best, but generally no pruning is needed and it certainly would not help the plant hold up the flowers, only support can do that.

Interesting our tree peony never has a problem holding its flowers up, our herbaceous perennial peonies on the other hand in some cases do.

Thanks i think i will try tying the spindly parts up with string to see if that helps
Thanks again

Paeonies, especially the big fat doubles, always seem to have this problem - they are very easily ruined by rain, and they do need proper supports that are driven into the ground when the plant is growing in spring time. You can buy them at all garden centres and on-line, but they always seem to be extraordinarily expensive to me for a few bits of wire. Driving in bamboos around the plant and tying string or garden wire round to contain the stems should do the trick. Do make sure you don't stick the bamboos into the rhizomes themselves, though! Once the leaves and flowers are fully grown, you can scarcely see the supports.
Tree paeonies are another thing altogether, however, and we used to have a beautiful one in our last garden, but the flowers were singles and didn't have nearly the same problems as ordinary ones with the weight of rain dragging them down. I shall be interested to hear how tying in the spindly bits works, and whether your flowers survive.

Just been trying and sucessful with some of the plant but there are parts that have grown really wierd as though the branch broke last year but didn't die and this year has grown an abundance of big flowers but if i try to raise it to tie to another part of the bush then you can hear a crack.
I think the best thing for me to do is to wait until autumn and try and cut it back a bit - unless you know that i shouldn't do that!
What I don't want it to ruin it

You can cut a tree peony to the ground if you so choose though it will produce a lot of green sappy growth that can't support the flower heads next year.