No idea how to plan for my itinerary

Dear guys,
I will be travelling to Japan for the first time in this coming mid of December. We will arrive Haneda airport at 2230 on 18th Dec and we will only spend 5 days there. Currently, we are planning to go Disneyland, Mt Fuji and no idea where else should we go. So we need help on the following queries:

1. We will be staying in the hotel near Shinjuku. Is it ok for us to travel to the city since we arrive at 2230 on the 18th?
2. We wish to visit some places outside Tokyo but we have no idea where is the best place that we should go considering the time constraint.We intend to book for our hotel stay for the 4 nights in Shinjuku but considering whether is there a need for us to overnight somewhere else just in case we travel outside Tokyo?
3.How should we travel from the airport to city centre as well as to the places of interest and the most economically way is preferred. (For instance, to Disney)
4. Is it possible for us to get private tour guide in Japan during our 5-day trip?

Thank you very much and hope to get more information about the trip.

Regards,
Stephy

You have no time to make inter-regional trip in Japan. So You should check out his page.
http://www.japan-guide.com/list/e1103.html

Transportation in Tokyo
http://www.japan-guide.com/e/e2017.html

I will be travelling to Japan for the first time in this coming mid of December. We will arrive Haneda airport at 2230 on 18th Dec and we will only spend 5 days there. Currently, we are planning to go Disneyland, Mt Fuji and no idea where else should we go.

I would probably spend some time exploring Tokyo itself!
http://www.japan-guide.com/e/e2164.html

If you think you would prefer other day trips then they are listed down the bottom of the above page.

1. We will be staying in the hotel near Shinjuku. Is it ok for us to travel to the city since we arrive at 2230 on the 18th?

Should be fine as explained here:-
http://www.japan-guide.com/e/e2430.html

2. We wish to visit some places outside Tokyo but we have no idea where is the best place that we should go considering the time constraint.

If you want to see Mt Fuji, then either Kawaguchiko or Hakone would be suggested:-
http://www.japan-guide.com/e/e6906.html
http://www.japan-guide.com/e/e5200.html
Click on the "access" sections to see how to visit from Tokyo.

We intend to book for our hotel stay for the 4 nights in Shinjuku but considering whether is there a need for us to overnight somewhere else just in case we travel outside Tokyo?

Depends where you go but both of the above could be done as a day trip, or as an overnight trip. Usually with a stay at a traditional inn/ryokan.

3.How should we travel from the airport to city centre as well as to the places of interest and the most economically way is preferred. (For instance, to Disney)

Disney:-
http://www.japan-guide.com/e/e3016.html
http://www.japan-guide.com/e/e3016_access.html

In general individual tickets will be the best option. It is usually more convenient to purchase a Suica pre-paid card:-
http://www.japan-guide.com/e/e2359_002.html

4. Is it possible for us to get private tour guide in Japan during our 5-day trip?

Private professional guides tend to be very expensive. There are some goodwill/volunteer guide options available. Usually not for all five days of course.
http://www.tokyofreeguide.com/

Enjoy your trip!