Is it permissible for a person to order from websites again, if they have atoned for the oath they swore not to order from them? And should a person avoid things they suspect they swore not to do, if they swear many oaths and forget what they swore upon?

The jurists differed regarding the breaking of an oath by someone who swore to abandon something and then did it forgetfully. The preponderant opinion is that he does not break the oath when forgetful. If you wish to offer expiation as a precaution, the matter is broad, and indeed, it is more cautious. According to the opinion that one breaks the oath and expiation becomes obligatory, then the expiation is not repeated if you request from the websites again, because the wording of your oath does not imply repetition except by intention. And expiation for an oath is not valid through fasting except when unable to perform the acts mentioned in the verse. If you doubt an oath, nothing is incumbent upon you, because the original state is the acquittal of responsibility.