Learn Finnish: Liha paloi uunissa. - The meat burned in the oven.

Actually, no! Paloi comes from the Type 1 verb palaa (to burn). In this lesson, you are learning that Type 2 verbs with a diphthong (like juoda) drop their first vowel to form the past tense (joi). However, for Type 1 verbs ending in -aa, the rule is to change the final a into an o before adding the past tense -i. So palaa becomes paloi. It looks just like our Type 2 past tense verbs, but it gets there via a different rule.

If palaa means "to burn", how would I say "I burned the meat"?

You would use a completely different verb! Palaa is an intransitive verb, meaning the subject is just burning or catching fire on its own (like the meat in this sentence). If you want to say that you actively burned something, you must use the verb polttaa. So "I burned the meat" would be Minä poltin lihan.

Why is the ending -ssa used on the word uuni?

The -ssa ending is the inessive case, which translates to "in" or "inside". The base word is uuni (oven), so adding -ssa gives us uunissa (in the oven). Because uuni contains the back vowel u, we follow vowel harmony rules and use the back-vowel ending -ssa instead of -ssä.