In season 6, we see that Ernie had his own dog Wilson, and for a while, resided at the Douglas home while they were in process of adopting the boy. But after the adoption was official, Wilson disappeared altogether. Was it because that they didn't want two dogs on the show?

Hard to know. Probably a writing error in the three part arc which brought Ernie into the Douglas family.

In season 6, we see that Ernie had his own dog Wilson, and for a while, resided at the Douglas home while they were in process of adopting the boy. But after the adoption was official, Wilson disappeared altogether. Was it because that they didn't want two dogs on the show?
I kind of think it was not wanting to deal with two dogs.

that and how does Ernie go from being in Chip;s class to later being not, but is in the class behind Chip ? if I remember correctly +-

Yes, that's the way it happened.

There's all kinds of examples from shows of that era, of changing kids' ages and grades. And why? Who knows?