Late night transport from Haneda

I know that this question has been brought up many times, but mine i guess might be the most late arrival.

I'll be arriving in Haneda Terminal 2 (international) on 00:30am late night. Plus all the immigration procedure, the earliest i can get out around 1am (which i doubt).

1. Any public transport still operating at 1am?
2. i will be staying in toyoko in Haneda No2, which is not far away (6km) around Ootori station. How much approximately will the taxi cost?

Thx in advance!

Train already overed. (last dep 0:23)

Taxi
: about 10min
: around 1700Y/4 adult passenger type most
https://www.anonimg.com/img/8a8e2011f99cff2bd3a3ad370e765be4.jpg
(This is not Taxi stand just waiting pool by driver)

If want larger type ask airport staff or hotel staff before.

(note)
Hotel name is "Toyoko inn" not "in".

No public transports operated at 25:00(Mon-Sun) in Haneda.

There is a "free" shuttle bus between Haneda and Toyoko Inn Haneda 2, but, the last bus departs Haneda at 24:12.
http://www.toyoko-inn.com/hotel/00042/shuttlebus.html

The taxi fares between 22:00 and 5:00(Mon-Sun) apply a night fare which 20% additional fee(it actually 20% less distance calculation but easy to understand as 20% additional). The fare will be 2,000 - 2,500 Yen.