I think this is a really complex principle that doesn't perfectly fit into a rule per se but there are definite differences in usage (although I havn't studied English grammar at a highly advanced level). I think the choice between the present participle (-ing) and the infinitive (to ...) is often largely determined by the preceding verb. In the example of the verb to like, either is equally acceptable, however I think there are often cultural preferences we lean toward. For example I would probably tend toward "I like cooking" rather than "I like to cook". Although this would be superseded by any previous conversation, as I would likely answer with the corresponding form based on the question asked of me. "what do you like doing?" or what do you like to do". With other preceding verbs this can however be more serious. For example "I stopped smoking" and "I stopped to smoke" have very different meanings.and you would never say "I quit to smoke". I am not sure that this can be easily tied into a rule, but maybe needs to be dealt with on a case by case basis. I generally encourage learners to use the present participle as the first port of call as this more often corresponds to the natural response if you are unsure and need to guess. I would love it if someone could enlighten me further.

Yes this is correct. You could also join the sentences, "I think being a cook is boring, because you have to cook every day."

You wouldn't really say "through the phone", instead of through we would use by, referring to the phone as a method. eg. by phone or by mail. stylistically I would also prefer all brackets at the end so as not to break apart the sentence, as it is clear which is a phone number and which an email. So you could say "you can contact me anytime by phone or email(000000, [email protected])."

I cannot think of an appropriate translation for this sentence, and there may just not be a direct translation in English. I think the sentence in itself is good, and could be used as it is but would require the explanation to follow as it is not a common phrase. Although I would say "the" capacity not "a" capacity. So for example you could say/write: "Some people do not have the capacity to be wealthy, money will make them arrogant and horrible." Alternatively in a much more casual chat, "some people can't handle being wealthy" may be an option. I would be interested to see what other people think too.

This comic is written in a form of old English, so it is not natural for conversation. In this context, it would mean "I am not able to pay, this large amount of money(so much), at the moment", if I were to borrow it from you. essentially, I will not be able to pay you back an time soon, as Mikkel said. However if I were to hear it spoken normally, I would guess the person was asking me whether they could pay back a loan in smaller increments, reducing monthly payments or asking for an extension.