Learn French: Tu devrais toujours agir avec bienveillance envers autrui. - You should always act with kindness towards others.

While les autres (the others) would also make sense, autrui is a slightly more formal, elegant way to say "other people in general." It is invariable (it never changes form) and is almost always used after a preposition, such as envers, pour, or à.

Could I use vers instead of envers for "towards"?

No, because envers is used for abstract, emotional, or behavioral attitudes towards someone (like showing kindness or respect). You use vers for physical direction, like walking towards a building, or for time, like "around" 3 PM.

Why is the verb devoir in the conditional tense (devrais) here?

Using the conditional turns "you must" (tu dois) into "you should" (tu devrais). It softens the obligation, making it a piece of advice or a moral recommendation rather than a strict order.

Is there an adverb form for "with kindness" instead of saying avec bienveillance?

There is the adverb bienveillamment (kindly), but it is quite long and awkward to pronounce. French speakers frequently prefer using avec plus a noun (literally "with benevolence") to avoid clunky adverbs.