Here are some definitions of go when used in different ways:
1.3 (go to) Attend or visit for a particular purpose: we went to the cinema
1 chiefly British An attempt or trial at something: have a go at answering the questions yourself
2 British A person’s turn to use or do something: I had a go on Nigel’s racing bike
When you go at something, you're attacking it, attempting it (have a go at it), or otherwise doing something to it other than simply visiting it.
For the purpose of this discussion, we would consider a website to be a place, so you would direct people to go to the website.
It is also idiomatic to say, for example, "Go on Facebook". However, this carries the sense of logging onto the site or needing to go through some process of entering your credentials, rather than simply visiting it.
So to answer your specific questions:
A or B: your sentence B ("go to ThisIsATest.com") would be preferred over sentence A ("go at ThisIsATest.com").
BrE vs AmE: I usually favour British English, but I believe American English speakers would concur with this conclusion.
to vs on: if you are directing people to a site, treating the site as the destination, use go to (or simply "visit ThisIsATest.com", leaving out go altogether). If you are including the notion of site access (passwords, etc), it could be argued that go on is in common use, but it would be better to say, "Go onto ThisIsATest.com", or better yet, "Log into ThisIsATest.com".