1) Question: "to infinitive" or "-ing"?
This is something students often ask about and it’s kind of a tricky point in English.
Here I’m going to illustrate the difference in meaning between the use of the “to infinitive” and the “-ing” form with two verbs: stop and remember.
stop to do sth (sth = something)
They were hiking in the mountain. Around midday they stopped to eat in a meadow.
This means that they were walking and then they stopped because they wanted to start a different thing: they wanted to eat their sandwiches.
There are two things combined: first they stopped walking and then they sat down and started eating their sandwiches.
So, in this situation “They stopped to eat” means two things in one: “They stopped walking and started to eat”.
“Stop to do sth” expresses two things: “stop and start”
Let’s compare this now to the “-ing” form
stop doing sth
You are reading a book and the phone rings. You stop reading and answer the phone.
This means that you were reading a book, and when you heard the phone ring, you stopped what you were doing (reading a book), because you wanted to answer the phone.
This is quite similar to the previous example, when you stop one activity to do another thing. The difference is in the focus.
“Stop doing sth” refers to the action that you interrupt, not the next action you want to start.
Other examples could be:
When the teacher entered the room the students stopped talking.
This means that the students were talking before the teacher arrived.
Compare this to “remember to do sth” and “remember doing sth“.
1) Please remember to switch off the light when you finish the meeting.
This means that you should remember that there is something you will need to do. (i.e. Please don’t forget that there is something important to do)
2) I remember seeing this film before.
This means that you remember something that you did in the past.
I hope these examples help you see the differences in meaning.