Learn Russian: Неужели ты не видел его степлер и скотч? - Have you really not seen his stapler and tape?

Because его is a third-person possessive pronoun meaning 'his'. Unlike words for 'my' or 'your', the third-person possessives (его, её, их) are indeclinable. They never change their form, no matter what case, gender, or number the noun they describe is in.

What case are степлер and скотч in, and why haven't their endings changed?

They are in the accusative case because they are the direct objects of the verb видел (seen). However, because they are masculine inanimate nouns, their accusative form is identical to their nominative (dictionary) form.

What exactly does неужели add to the sentence?

Неужели is a particle used to express strong surprise, disbelief, or doubt. While a standard question just asks for information, adding неужели turns it into 'Have you really not seen...?' or 'Is it actually possible that you haven't seen...?'

Is скотч literally the English brand name 'Scotch tape'?

Yes! In Russian, скотч has become a generic word used for all kinds of adhesive tape, regardless of the actual brand.