I know a little bit of English. I'm somewhat rusty, but let me try.
"im in uk and i need a question"No you don't. You have two of your own.
"will uk batterys work with a american ds"The DS won't be using any commonly-available battery type. They use a rechargable type that was made just for Nintendo. The batteries will be the same, whatever country you buy them in.
"also with the ac adaptor wotk in a uk socket if i use a travl adaptor"The AC adaptor is the thing that recharges the battery. If you have a travel adaptor, and it converts power to let you plug in American devices, then yes, it would probably let you use the American AC adaptor in the UK.
Also, you might like to hear that the battery in the DS is very similar to the battery in the GameBoy Advance SP (not exactly the same), so while you can't use a GBA SP's battery in the DS, you can use the SP's AC adaptor to charge the DS's battery. So if you have the AC adaptor from a local GBA SP, then you can just use that adaptor on an imported DS.