I would like to know IF these are correct.

1. It is almost half the size

2. He is almost half MY age (for instance, I am 40 year-old and my son is 19 year-old) 'It is almost twice the size' is good.

Not quite - you don't need the indefinite article "a" before half when half is used as an adjective to describe size. It is almost half the size. I am 40, and my son is 19. Wow, he is almost half my age. I cannot believe where the years have gone. Note while half can be used as an adjective, a quarter and a third, and other fractions with "a" do not have the same adjective form. This bag is a quarter of the size of that one. However, you can form an adjective of any fraction in the following way: one-fifth the size, two-fifths the alcohol, three-quarters the length, etc placed before the noun and with a hyphen This bag is three-quarters the size of the other one.