Learn Finnish: Me laitetaan selkäsuoja päälle ja mennään ulos. - We'll put back protectors on and go outside.

This is the distributive singular syntax you are currently learning. Because each person in the group is putting on exactly one back protector, Finnish uses the singular form. If you used the plural selkäsuojat, it would sound like each individual person is putting on multiple back protectors at once.

Why doesn't the object selkäsuoja have an accusative ending like -n?

The verb here is in the passive form (laitetaan), which spoken Finnish uses to mean "we". A major rule for total objects is that they do not take the -n accusative ending when the verb is passive. Therefore, the singular object takes the base form and looks exactly like the nominative.

Is it normal to say me laitetaan and mennään instead of the standard me laitamme and menemme?

Yes, it is the absolute norm in spoken Finnish. In everyday speech, the passive form has almost completely replaced the standard -mme form for the first-person plural. You will hear this structure used constantly by native speakers.

In previous examples, putting on a hat was laittaa päähän. Why does putting on a back protector use päälle?

It depends on where the item goes on the body. A hat goes specifically onto the head (päähän). For items of clothing or gear that go on the torso, back, or cover the body generally, Finnish uses päälle (literally meaning "onto").