The first is fairly common when speaking about someone's circumstances, such as their financial state, their job title, or their history. Basically it refers to being in someone's shoes, so to speak.
He's buying a brand new car with all those debts he has? I wouldn't do
that if I were in his position.
The second isn't common at all and the only way it works is if you're talking about someone's physical location. I can't even think of a good example for it.
John's on the US/Canadian border and he's going back into the US? I
wouldn't do that if I were at his position.
It seems that nobody is going to answer, so let me try.
It's a bit difficult too for me to understand the difference but let me simplify your example.
I think that we can represent the same meaning with two different structures.
(1) The future worries me
(2) I worry about the future
According to Cambridge Dictionary
In the first case, we got
worry [TRANSITIVE]
to make someone feel unhappy and frightened because of problems or
unpleasant things that might happen
In the second case, we got
worry [INTRANSITIVE]
to think about problems or unpleasant things that might happen in a
way that makes you feel unhappy and frightened
Let's take a look at Oxford Dictionary
Feel or cause to feel anxious or troubled about actual or potential
problems.
[no object] he worried about his soldier sons in the war
[with object] there was no need to worry her
Feel [INTRANSITIVE]
Cause to feel [TRANSITIVE]
Knowing all this, let's return to your example
People have a variety of factors in their lives that cause them to
worry
[Simplifying] A variety of factors worry them. [TRANSITIVE]
I found myself worrying about the tests
[Simplifiying] I worry about the test [INTRANSITIVE]
about the test is NOT the object, it is a prepositional-clause.
Best Answer
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.
Here you is an object, and the whole things means that you don't want to cause the person to worry.
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.