Yes, it is. To make it easier, let's go to the four examples (slightly modified) given in your original post.
- Poczuć to, co czują inni.
- Chroń to, co dla Ciebie ważne.
- Ubierz to, co chcesz.
Why is there this TO here?
- Nie wiem, co [on] robi.
Why there is no TO here?
In the first three of them, you are indicating a limited
set of items or things (you want to feel a limited number of things, namely those that others "feel"; you want to protect a limited number of things, namely those which are important to you; you advise someone to choose items to wear only out of those your friend has at her disposal at a particular moment).
In the fourth example, you are indicating an unlimited
set of possibilities that a person might be exercising at the moment you are making your statement; you have no idea whatsever what these could be.