What's the difference between בפנים and בתוך?
Inside something is בתוך. You wouldn't use it alone, you would give context.
Just inside,without context, is בפנים.
They are not interchangeable.
Adding ot what NaftaliFri1 says, you need a noun after בתוך because it's a preposition. בתוך המקרר.
Ha-gever omed bifnim.
Why is it בפנים and not בפני
Because בפנים is just the Hebrew word for "inside" as a stand-alone location specification. Not sure what בפני you have in mind.
Because it sounds plural.