Another question about JR Pass

We will arrive in Narita at 4pm on 20 Dec. We plan to take a limousine bus, from Narita to the hotel in Ikebukuro area (considering it's more convenient, as the bus will take us direct to the hotel). I have JR Pass for 7 days. And we will start our trip to Kyoto and Osaka, on 22 Dec. My question:
When should we change the Exchange Order to JR Pass? on the arrival date 20 Dec at the airport? or wait until 22 Dec?

On the day we get JR Pass, is it considered as the day 1?

When should we change the Exchange Order to JR Pass? on the arrival date 20 Dec at the airport? or wait until 22 Dec?

Unless you think that there is a possibility for you to change plans between the 20th and the 22nd, I recommend to exchange it on the 20th. You will then be able to make seat reservations. But if your schedule allows for a more convenient exchange on a different day at a different location, for example, on the 21st at Tokyo Station, you may also do it there. Or on the 22nd before departure. Most of all it depends on your schedule.

On the day we get JR Pass, is it considered as the day 1?

You specify day 1 when you exchange the voucher.

You plan to take the Limousine Bus from Narita Airport to your hotel for greater convenience. But, you did not say how long you'll be in Japan and if you'll depart from Narita or Kansai Airport.

The answer to your question, "When should we change the Exchange Order to JR Pass?" depends on how many days will you be in Japan and if more than 7 days, will you have long distance train travel after the 7th day? If so, when and from where to where?

Your 7-day JR Rail Pass starts from the date you want it to become effective. The effective or start day becomes day 1 and expires at the end of the 7th day. When you exit through the manned gate, you must show your JR Rail Pass and the expiration date cannot be later than the 7th day.

If your stay in Japan is less than 7 days you should use Narita Express to Ikebukuro and catch the taxi to your hotel since JR Rail Pass covers Narita Express. Using the Limousine Bus is an additional cost when you have JR Rail Pass.

Additionally, if your stay in Japan is less than 7 days OR completing long distance train travels within the 7 days, then, making the Rail Pass effective start date on your arrival date is not an issue. But, if your stay in Japan is longer than 7 days such as 9 or 10 days and if you require a lot or long distance train travel anytime after the 7th day, you may want to delay the effective start date of your JR Rail Pass to when you're going to Kyoto/Osaka.

As for making your train reservation to Kyoto/Osaka on Dec 22, there's always the risk that seats may not be available on the train that you want if you make your train reservation later. Then, you can reserve a later train or ride the un-reserved seat car.

If you have more questions, post your questions and someone will respond.

I would also exchange the voucher early for the reason stated by Uji, it is always nice to have reserved seats and there is no problem reserving seats with the rail pass while it is not valid yet provided the date you want to travel is covered by the validity of the pass, of course.
And Harold raises a couple of good questions, we don't know your schedule but given the fact that Limousine buses are about as expensive as the NEX you might want to consider covering Narita - Tokyo by the pass and use a taxi from the Ikebukuro station to the hotel but that all depends on how you intend to use the pass the rest of the period.