I thought this would be "אני בתוך את המסדעה שלהם", don't you need the "את" as I (as a subject) am speaking about an object?
It's not the object of a verb so no.
Am I right in thinking that this is because "בתוך" is a preposition and not a verb?
the word בתוך serves as the preposition "in" (indirect object/dative), so you cannot use את here, which is the preposition for the direct object/accusative.
Why not בתוכה?
Because בתוכה is like "inside her" (or "inside it", which would be the case for "restaurant", translating to English). You wouldn't say "I am inside it the restaurant". Or the subject, or the pronoun, not both.
Why isn't is "אני בתןכי
oops....I didn't answer it correctly...silly
Could I say "אני בתוך מסעדהם"?
Why is this sentence given wrong? Its not clear if its m or f