There is no single translation that will work in all cases. I won't cover all cases here: I will concentrate on how to specify definitions but mention a few related points.
Most dictionaries will translate a verb or verb phrase using an infinitive or infinitival phrase. However, most will omit the "to": keep promises ...
Eating, drinking and sleeping at this location is prohibited
might feel acceptable because:
the structure is imitating what would be found in the case of participles being reduced into a nounphrase by conjunction reduction
"at this location" restrictively and independently modifies three items in a list, which feels quite strange
If, for example,...
The meeting might be in the future, but the act of "postponement" can be in the past.
So it is correct to say:
Yesterday I postponed our meeting until the end of the month.
I have postponed the meeting.
In these sentences "meeting" is a noun. It's not a gerund.
Now you can also postpone actions.
In these cases you use the gerund, ...
In the first case of I like to play cricket simply indicates that it's my intention to play cricket in a certain situation/condition.
It also means that I prefer cricket to other sports.
In the second case: I like playing cricket means it's my passion/hobby/regular habit to play cricket.
She had been horse-riding
She had been going horse-riding
mean the same thing.
I cannot tell you why the computer did not accept your version, which tracks the original sentence, except to say that computers are very stupid beasts.
I should also point out that “horse-riding” is not idiomatic American English.
ride a horse
is idiomatic in American ...
Interesting question. I think the expression "go [verb]ing", where the verb is a sport or leisure activity, has a suggestion of "go to the place where such an activity happens". Rebecca spent the afternoon riding, not going to the stables. The author could have said that Roger 'went swimming', but he only went to the pool once, so he ...