Frogs are capable of retracting the eye, it's where they squish the prey with as well.
When looking inside the mouth you'll see the bumps from the eyes as well.
Might be it is somewhat irritated or something like that.
Personally i don't see anything disturbing, but you might wan't to shoot the question to a specialized vet like blueisallyouneed suggested already.
Normally when something is wrong with the eye, like infection, the frog pulls it's inner eyelid over the eye, making it look somewhat thick and milky.

For the part of spitting out food.
It's something i see with lots of frogs.
Mostly when you just acquire a frog that has had little variaty in food,
they need to "taste" particular insects a couple of times first,
same thing with juveniles.
It looks like they are horrified by the taste,
but if you keep offering the food source from time to time they will eventualy eat it without spitting it out.
In some cases i even saw a frog let it's tongue fall out with the insect attached and scrape it off with the front feet.
No idea what it is exactly causing them to do so, but they will get used to it.
All of my frogs big enough eat phoenix worms without any problems, don't even pierce them on front hand.
The horror stories of live insects eating out of the frog or ending up in the stool are just BS.
Frogs also have gastric acid, pretty darn insect coming out of that alive