means to, over a period of time, think about the consequences of two or more choices in a decision. If there is only one thing you are pondering, you are pondering whether or not to do that thing.
to mull over
is the same as ponder - but you can mull over collective nouns, meaning you are trying to decide which one of the group. "I mulled over the candy, and found a good piece."
means to think about the consequences of something carefully, thoroughly, and for a long time. Typically when you contemplate something, you are deciding whether or not to do it, not picking among an array of choices. It has a serious connotation, likely due to the common phrase contemplate suicide.
I don't hear this word a lot. According to Google, it can be used intransitively, so you don't have to be cogitating about anything in particular. The other words here generally require a "target" to make sense.
to deliberate [on]
means the same as contemplate. When I hear this word, I think of court proceedings or meetings ("the jury will deliberate... etc.").
I don't hear this in speech very much. In my opinion it's a "less serious" version of contemplate.
to dwell on
means to think about something over and over. It could be the consequences of a decision not yet made, a decision that just has been made, or it could be going over past events in your mind. Dwell on can have a negative connotation, possibly that what you are dwelling on is bothering you or haunting you.
So, I would answer like this:
("depth 10k worths" doesn't make sense to me, so the second is a guess)
I have been dwelling on my son (all day) since he left home for college.
I have been mulling over my depth 10k worths because I will have to pay it by next week but I don't have enough money. So I have to find a way.
I have been dwelling on my new school project. I don't know where to start.
The government deliberated how to stop protest on raising student fees.