Why is the "ar" there?
Because tháinig ar is how you say "found".
You can see that the literal translation "I came upon the website" also uses ar/"on".
Yeah, after I wrote this I saw it a few more times and figured it out. Thanks.
what's wrong with "fuair mé ..."
Either tar ar or faigh could be used, so Fuair mé an suíomh gréasáin (without an ar ) should be acceptable.
Is "D'aimsigh mé an ..." acceptable?
It should be, but I have just tried it and it was not accepted. Nor was 'suíomh idirlíon' for website.