Trains between Haneda and Narita.

I need to find out how late the trains run? It is hard to tell from the websites for the trains and the different lines. I have a group of 24 to get these trains, i need to be sure we get the right ones, and that they run past 23:00 at night.

The last connection from Narita Airport to Haneda Airport:
22:16 depart Narita Airport by Sobu Line
Transfers at Tokyo, Shinagawa and Keikyu-Kamata Stations
00:27 arrive at Haneda Airport

Haneda Airport to Narita Airport:
20:51 depart Haneda Airport by Keikyu Railways
Transfer at Keisei-Tsudanuma Station
22:56 arrive at Narita Airport

There are later connections if you go only as far as Narita Station.

You can look up connections yourself on the following website:
http://www.jorudan.co.jp/english/norikae/

Also, can anyone tell me, can you book your ticket the whole way at the start of your journey or do you need to purchase tickets at each stop?
would it be better to reserve beforehand?

Also, can anyone tell me, can you book your ticket the whole way at the start of your journey or do you need to purchase tickets at each stop?

It depends on the route. It might be possible to buy a "transfer ticket" for the whole journey if you travel along the Keisei-Toei-Keikyu corridor. However, if you use any other route, you will likely have to buy multiple tickets along the way.

would it be better to reserve beforehand?

Trains along the route do not allow seat reservations.