Learn Finnish: Vaellamme mieluummin metsässä kuin treenaamme kuntosalilla. - We would rather hike in the forest than work out at the gym.

Yes. When you use mieluummin ... kuin to compare two actions you are performing, both verbs must match in tense and person. Here, both vaellamme (we hike) and treenaamme (we work out) are in the first-person plural. You cannot leave the second verb in its infinitive form.

Could I express this same idea using the verb pitää (to like)?

You could, but it requires much heavier grammar. With pitää, you would need to turn both verbs into -minen nouns in the elative case: Pidämme enemmän metsässä vaeltamisesta kuin kuntosalilla treenaamisesta. Using mieluummin with standard conjugated verbs is a much more natural and efficient way to express a preference between actions.

Can I put mieluummin at the very beginning of the sentence?

Usually, mieluummin acts as an adverb modifying the first verb, so it sits right after it (vaellamme mieluummin). Putting it at the very beginning of the sentence is grammatically possible but changes the tone; it sounds defensive, like you are emphatically correcting someone who just suggested the gym.

Why is there a double 'l' in vaellamme when the dictionary form is vaeltaa?