The stove should be pretty much flush, you only need enough space to be able to slide it in and out as needed. The side of the stove shouldn't get hot enough to affect the glue.
As for the food falling down between, yes that can be a problem. I once found an aluminum T shaped piece that straddles the gap to close it off. I believe it was at Menards.
"The difficult we do immediately... The impossible takes a little longer" - Grandpa
Don't worry about nothin', aint nothin' gonna turn out right anyway" - Dad