No, not all verbs can be used with those pronouns. I know them as "pronombres reflexivos", which are used with "verbos reflexivos". This is somewhat similar to adding "myself, yourself, himself, herself", etc. to verbs in English.
I have to say that in Spanish, even though not all verbs are "reflexivos", there sure are a lot of them ha ha ha! In English, it's not that common, but in Spanish it is. Some examples where we use them and English does not: "Yo me peino (I brush my hair)" "Ella se retrasó (She's late)" "Me di cuenta que estaba equivocado (I noticed that I was wrong.)" "Me estoy aburriendo de esta reunión! (I'm getting bored with this meeting!)"
To practice, look up "verbos reflexivos en español" and see which verbs are used with those pronouns as opposed to English. Some will be used similar to English, like "Me acabo de golpear! (I just hurt myself!)" so they will be easier to remember, but some you just have to memorize that they use the "pronombre reflexivo".