Am I going to the right place to apply for my ED Visa in Vientiane?

That’s right. Good luck to you! I was there on a Monday and it’s the worst day (longest lines).

I recommend going at 11:00am ... big big queues start at 07:30... last time I was there , no queues at 11:00am.... but it does mean you have a high ticket number .. your ticket number will come up later in the afternoon on the following day for visa collection ... but this ok too ... you don't go a queue again at 13:00 like everyone else ... go have a nice lunch ... roll up at 15:00 .. less people waiting - more free seats

Seeing as the thai consulate in Vientiane is the busiest one in any nearby country you aren't gonna be the only foreigner slogging there :O Follow the herd ;)

Yes, you get visa at the consulate not the embassy

Correct