Are the sentences below correct?
1- This morning the postman was chased down the street by my dog. yes
2- The child hurt himself badly when he fell out of the bedroom window. yes
Other options are "out from", "down", and "over".
3. He insisted on being given a receipt for the bill he had paid. yes
4. Fewer people go to football matches now than twenty years ago.
Does the word "lesser" exist? It does, but it means less important and doesn't refer to number. Colloquially, many would say 'less people'.
5. Could you please tell me if you have any electric typewriters in stock. yes
Could we say "in store"?
6. The factory paid out nearly a million pounds to their employees who were injured in the explosion. yes
And last but not least, is it correct "he suggested to me go on holidays" or "he suggested they go on holidays"?
How does exactly work the verb suggest?
He suggested (that) they went on holiday. note that after the preposition 'on, we do not use the plural here
He suggested (that) they should go on holiday.