Learn Finnish: Liha säilyy pakastimessa niin kauan kuin haluat. - The meat stays fresh in the freezer as long as you want.

There isn't one! The verb säilyä means "to be preserved", "to keep", or "to remain in good condition". In the context of food, saying se säilyy is the standard Finnish way to express that "it stays fresh" or "it keeps".

Does the phrase niin kauan kuin require any special verb forms or moods in the clause that follows it?

No, it doesn't. Unlike some languages that require a subjunctive mood after phrases like "as long as", Finnish simply uses the standard indicative mood. Here, haluat is just the regular present tense for "you want".

Why is the word for "in the freezer" pakastimessa? Why isn't it "pakastinissa"?

The basic dictionary form is pakastin. Nouns ending in -in (which are often instruments, tools, or appliances) change that ending to -ime- before adding a case ending. So, pakastin + -ssa becomes pakastimessa.

Could I use kunnes (until) instead of niin kauan kuin here?

Not naturally. Kunnes focuses on the exact endpoint when a state changes (until you want it). Niin kauan kuin (as long as) focuses on the ongoing duration of time that the condition remains true, which makes much more sense when talking about how long food will continuously last.