Learn English – The usage of at the back/front side

It's probably worth noting straight away that "to get" is increasingly common in OP's context. As this link shows, X got me interested in Y was virtually unknown a century ago, but it's now far more common than made me interested in.

But there are subtle syntactic and semantic differences. As noted above, of OP's first pair...

1: This book got me interested in Buddhism.
2: This book made me interested in Buddhism.

...#1 is more common, but both are acceptable. And so far as I'm concerned, they mean the same. But...

3: This book got me thinking about my future
4: This book made me think about my future
5: ✲This book made me thinking about my future (where ✲ marks a usage as unacceptable)

...with OP's second pair we can't just replace got with made. Notice also that we can explicitly use the "marked infinitive" (to think) with got (also to [present participle], but I don't know what to call that)...

6: This book got me to think about my future
7: ✲This book made me to think about my future
8: ?This book got me to thinking about my future (perhaps not everyone would accept this form)
9: ✲This book made me to thinking about my future

On the basic of the above, I suggest it's well worth learners spending some time becoming familiar with the syntactic possibilities of to get. Because it's increasingly common in modern speech, and can probably be used in more contexts than to make, it's likely to be more useful over the long term.

On the semantic front, note that to make often carries implications of deliberate and/or forceful actions. Thus with this pair...

10: He got me to eat snails in garlic butter
11: He made me eat snails in garlic butter

...there's a much stronger implication that in #10 he persuaded me (possibly quite easily). It would be quite reasonable for the utterance to continue with "...which I really enjoyed". But #11 implies he forced me (much against my will). That one might continue with "...which made me feel really queasy".

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.