That snake looks like it has downs, I've never seen one like that. What species is it?

Its a hognose.

It's cute, in a ironic sort of way. Like a pug.

That snake looks like it's eye moves, I know snakes don't have eyelids, but are they able to move their eyes?

lmgtfy.com/?q=can+snakes+move+their+eyes%3F

The muscles needed to look around is functional in some but not all snake species, mostly vipers to make hunting easier.

I think so. you think I would know, having bred snakes for all my life.

Then you're someone who knows about snakes. I've always been iffy about them because, no matter what, I can NEVER tell their emotion, do snakes actually show affection towards their owners?

People say they don't, but that's a dirty lie.
Snakes will even show a reaction to their owners emotions. But I'm not sure how they tell what your emotion is.

All I know is, if you're distressed or angry when holding an unfamilliar snake it will most likely be scared of you or aggressive towards you.

So, like the snake above, like that finger patting it's head, they'll act excited or affectionate like most any other animal?

They don't usually like their heads touched, but they will often rub against you, which can be considered a show of affection.

My snake would always rub against my nose and sideburns.