4) 'I don't allow (smoke) in my drawing-room - smoking
I don't allow my family (smoke) at all - to smoke'
You either use 'allow + -ing form' without an object, or 'allow someone to (verb)'. So:
I don't allow smoking in my drawing room.
I don't allow my family to smoke in my drawing room.
I don't allow smoking at all.
I don't allow my family to smoke at all.
5) 'I used (make) fire by (rub) two sticks together - I read here http://www.really-learn-english.com/used-to-infinitive-gerund.html
that we use infinitive when somebody is used to do something but now he/she doesn't do it. And gerund is used when we're accustomed to do something and feel okay about it. In this example it doesn't say that the person doesn't make fire by rubbing two sticks any longer, so why do we use "to" here?'
You use the infinitive when somebody USED to do something, in the past, not when they ARE USED to doing it in the present. 'Used to (verb)' is made up of the auxiliary verb 'to use' in the past, plus an infinitive verb; therefore, the 'to' that follows 'used' is not part of the phrase, so much so that you have to conjugate 'to use' properly if the sentence requires you to; for example, 'I didn't use to (verb)'. 'Be/become/get used/accustomed to', on the other hand, has 'to' as a fixed part of it, so it requires a noun after it, and for a verb to be a noun, it needs to be in the -ing form. Also, you can conjugate the main verb as well and create sentences in the past or future. And, to wrap it up, 'by' is a preposition, so any verb after it needs to be in the -ing form. So, some combinations for you to grasp them all: