Worry is a verb and a noun, and worried is both the preterite (simple past) and past participle of that verb, and an adjective (as with many past participles).
When used as a verb, worry can take a normal object or a prepositional phrase.
I don't want to worry you.
Here you is an object, and the whole things means that you don't want to cause the person to worry.
I worry about you.
Here, about is a preposition indicating a topic. Just like you can "talk about going to the zoo", you can "worry about going to the zoo". It shows what the worry concerns.
You can use all the normal tenses with the verb worry, but you can also use worried as an adjective. If someone is worried, they are experiencing worry in the noun sense - an emotional or mental state associated with worrying. Both the noun and adjective sense can take a prepositional about, just like the verb.
If someone is worried about something, that is largely equivalent to saying that they worry about that thing.
All of your examples are correct and appropriate.
There are some other senses of worry, but they are sufficiently rarely used that I wouldn't worry about them for now.