Learn Finnish: Puistoon lisättäisiin valaistusta. - Lighting would be added to the park.

It is the conditional passive form of the verb lisätä (to add), meaning "would be added". To form it, you take the passive stem lisättä- and add the passive conditional ending -isiin.

Why is valaistusta in the partitive case? Don't objects of passive verbs usually take the nominative case?

You are correct that whole, countable objects of passive verbs usually take the basic nominative form. However, valaistus (lighting) is an uncountable mass noun here. Because it represents an unspecified or ongoing amount, it must stay in the partitive case (valaistusta).

Why use puistoon ("into the park") instead of puistossa ("in the park")?

In Finnish, the verb lisätä (to add) acts as a movement verb because you are directing something into a place. Therefore, it requires the illative case (puistoon) rather than a static location case like the inessive (puistossa).

Why does the sentence start with the location (puistoon) instead of the thing being added (valaistusta)?

Finnish naturally puts the known context or location at the beginning of a passive or existential sentence to set the scene. Starting with puistoon establishes where we are looking, and placing valaistusta at the end highlights it as the new, important information being introduced.