Learn English – What’s the English phrase to describe men who are standing next to each other, facing in opposite direction),

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.

In my opinion, the sentence has 2 issues.

1. 'Have learnt English' implies that you have done with your learning 2 years before. In this case, if you want to express "something has been happening", you could put it as "have been learning English"

2. 'Since' is used with a point in time. '2 years' is not a point of reference in the past. You could use "for 2 years" to indicate you've kept learning in the past 2 years. I am not sure if "since 2 years ago" works here. I saw some debates on the validity of "since 2 years ago" on some websites.

So, the whole sentence could be rephrased as: I have been learning English for 2 years or I have been learning English since 2 years ago.(I guess some would take issue with the latter sentence.)