"It is red on the inside."
Translation:Den er rød på innsiden.
Would the form change with context?
"Ser du huset? Det er rødt på innsiden."
"Ser du sitronen? Den er gul på innsiden."
In the first example the neuter forms are used, as you're talking about the house (huset), which is a neuter noun. In the second example the masculine forms are used, as you're talking about the lemon (sitronen), which is a masculine noun.
The genders have to agree:
"Det er rødt" (as you stated, is correct)
"Den er gul" (the masculine/feminine form of the adjective must be used)
Oh, that was a typo.
In terms of everything else though I am correct?
As in, I was asking about it changing from det/den depending on whether the previously mentioned noun is masculine/feminine or neuter.
Indeed. If there is no previously mentioned noun, e.g. you want to introduce a new noun, you use 'det'.
"Det er en sitron. Den er gul."