Born/Live

I.

  1. He was born on the third of August.
  2. He was born the third of August.
  3. He was born last year.
    Please correct.
    II.
    We have no house to live.
    We have no house to live in.
    Please correct.

I - all those forms are used.
II - only the second option is correct. You could also say ‘We have no house in which to live’.