Utilising of 7D Rail Pass

Hi

Need help here on when to start utilising the 7 days rail pass to save cost. My itinerary is like this:

23dec - Arrive in Haneda airport at 10pm

24/25 Dec - Disney Land/Sea

26-26-28 Dec - Kyoto/Osaka

29-31 Dec - Tokyo

My qn is if I start using on the 23rd, it'll be only a one way trip from airport to tokyo cos is already at nite, don't think will venture out anywhere else. Isn't worth utilising? How much will be the cost of one way train from Handeda airport to Tokyo/Shinjuku for 3 adults 1 child?

If starts 23rd, does it mean that the pass will expire on 29th?

Lastly, may I ask in Japan do they judge a child by height or age? Cos if a child is small in size at age 13, do we have to buy an adult fare or can be child fare?

Thanks in advance for valuable advise :)

You should not judge based on the time of the day but on the cost saved if using a Japan Rail Pass versus not using the pass.

How much will be the cost of one way train from Handeda airport to Tokyo/Shinjuku for 3 adults 1 child?

It is explained here, but note that the Japan Rail Pass is not valid on the Tokyo Monorail and Keikyu:
http://www.japan-guide.com/e/e2430.html

If starts 23rd, does it mean that the pass will expire on 29th?

Yes. It can be used from the 23rd through the 29th.

Lastly, may I ask in Japan do they judge a child by height or age?

By age. Or more accurate: by whether they are still in elementary school or not. But the latter rule is complicated to apply on foreign visitors, because the school system is different.

In case of the Japan Rail Pass, though, it is strictly judged by age: 12 and older pay adult fare.

Cos if a child is small in size at age 13, do we have to buy an adult fare or can be child fare?

13 is definitely too old for child fare.