Assalamu alaykum, are we supposed to pay khums on investments (if you need to know more specifically it's a UK investment ISA)? If so, on which amounts do we pay the Khums, and would this be every year? Are we to pay khums on the profit generated? Please shed some general light on this issue

If your capital is from clean money (Khoms paid), then, you just need to pay the khoms of the profit you get at the end of the year, if the profit is saved and not spent during the year.
On 01.01.2020 you received a profit of US$ 1000, which you kept a side.
You have to pay its khoms on 01.01.2021