A note to complete your infinitives and gerunds explanation:
To + ing form
To is really two different words:
1. A sign of the infinitive.
2. A preposition.
So, when to is a preposition and it is followed by a verb, we use the –ing form.
Ex. I’m looking forward to seeing you at Christmas.
Do you object to working on Sundays?
I’m no used to driving in
I prefer riding to walking.
If you’re not sure whether to is a preposition or not, try putting a noun after it. If to cannot be followed by a noun, it is not a preposition and –ing is not used.
Look forward to + ing
Object to + ing
Be used to + ing
In addition to + ing
Be accustomed to + ing
From English Grammar in Use. Murphy.