I know they would have written in hieroglyphics, but what was their spoken language like? Would the hieroglyphics be spoken in a certain way? Is it similar to any modern language today?
Egyptian was a Afroasiatic language. This language family is spoken at present across southwest Asia and north and northeast Africa. It includes languages like Arabic, Berber, Hausa, Hebrew, Somali, and, of course, Egyptian.
Eventually, Arabic replaced Egyptian as the main language spoken in Egypt. However, Egyptian itself continued to be used, eventually becoming the Coptic language, which is still has limited use as the liturgical language of the Coptic Church.
So first a brief bit on hieroglyphs. They are a mixed logographic-phonetic system. This means that some symbols represented sounds only, while others represented entire words or morphemes--the smallest meaningful unit in a language, which could be a word, but could also be something like a prefix or a suffix, like the plural marker -s in English. While at their base the phonetic portions seem to represent only single consonants, much like the Arabic abjad only has consonants, there are many symbols which contain more than one consonant.
Note that Egyptian, especially later on in the history of Egypt, was not written only in hieroglyphics, but in a number of other scripts, including Hieratic and Demotic, which are based on, but quite different from Egyptian hieroglyphs.
We know a bit about what it sounds like, from what we've deciphered of hieroglyphs and its later scripts, and also from comparing it to other Afroasiatic languages. However, there's a lot we don't know. This is in addition to the fact that Egyptian undoubtedly, like all other languages, changed over time, and that it was around for over two millennia.