Can you start a sentence with ‘As well,’ ?
Note the comma. I doubt anyone would argue about “As well as XYZ, blah blah.” But can you say “Joe did XYZ. As well, blah blah.”
I say you can’t, but what do I know?
You can, but it’s probably wrong. Even if it’s not, it sounds bad. But they probably do it in the UK, where the language is less refined.
As well water around here is contaminated, I recommend you buy bottled.
I thought that was an American English thing. It certainly isn’t recognized as correct usage in real English. 
Seriously, no.
I agree. It’s wrong.
As well, it looks really silly. See?
As well as I can tell its swell.
I dont think you would start a paragreaph with it, but mid paragraph, supporting a point - OK.
I don’t agree. As well, you’re wrong.
You mean like that?
As well as that dog looks, it still needs to see a vet.
As well as being a berk, I am also a moron.