Learn English – use “I start school at 8 o’clock every day” meaning “I start classes at 8 o’clock every day”

to ponder

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."

to contemplate

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.

to cogitate

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.").

to ruminate

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.

The words can often be used interchangeably. They have subtly different meanings that you should keep in mind when using them -- but don't assume a speaker or writer who is using them understands the difference!

"Assume" implies a bit more finality than "presume." It is more appropriate when a decision has been made, or is about to be made, with incomplete information.

"We didn't know how many people would be at the event, so we assumed that 100 chairs would be enough. (the decision was made)
"Since you didn't reply to my earlier email, I assume that you will not be joining us at the meeting." (implies that the speaker is ready to act without additional feedback from the recipient)

"Presume" gives a bit more room for the listener to correct the speaker. Using "presume" instead of "assume" adds an implied "but correct me if I am wrong" to the end of a statement.

"I presume you want chicken for dinner[, but correct me if I am wrong]."

In the past tense, "presumed" carries a bit of humility (if referring to oneself) or judgment (if referring to someone else), and it may imply that the presumption was incorrect in hindsight.

"I presumed that she would not object[, but she did object]."
"They presumed to know my intentions[, but they did not]."

"Assumed" is more neutral, and does not imply anything about the outcome of the assumption. If you want to communicate that the assumption was correct or incorrect, that fact will need to be made explicit.

"I assumed that the dog would not bite. I was wrong."
"She assumed that there would be enough cookies, and she was right."

The following examples contrast the two words and explain their implications:

Present tense:
"You have not told me what kind of ice cream you want. I assume vanilla will be fine."
(Even if the listener says nothing, the speaker will give them vanilla ice cream)

"You have not told me what kind of ice cream you want. I presume vanilla will be fine."
(The speaker would like the listener to confirm or reject the presumption. They will probably wait for an answer before giving the listener any ice cream)

Past tense:
"Alice assumed I would like chocolate cake for my birthday."
(The speaker may or may not have liked chocolate cake. It would be risky to guess without more information)

"Alice presumed I would like chocolate cake for my birthday."
(This is a subtly judgmental statement. Alice probably got it wrong.)

Final Disclaimer:
All of this is based upon present day, American usage. The words could carry different connotations in other countries or in older usage.