City/hotel Q night before Haneda Flight

I am flying out at 9pm Haneda airport.
I don't have to be at the airport until 5 or 6 pm.

Q1 Should I stay at a Haneda import Hotel and go to the airport early for shopping? Is there lots to see?

Q2 Stay at a hotel in the city the night before ? If so,
can you suggest which city?

Q3 does it really take only 35 mins to commute to Haneda Airport from Tokyo?

Q1: It's an airport. It has airport things. Shops, restaurants, etc. but really shoppings all there is to do. I'd suggest planning an activity for the morning/early afternoon, then give yourself extra time to get the the airport. Then you can shop if you're fine on time.

Q2: The city you should stay in is Tokyo. The area depends on your interests. If you are already staying in Tokyo the previous day, just stay the last night in that hotel like usual. If not, you can choose based on your interests. Tokyo Station, Shinjuku Station, Ueno Station etc. are all popular choices. I recommend on the Yamanote Line to make things easier, or you could stay in Yokohama for something different. It's up to you.

Q3: At least 30 minutes, or more depending on the station. Check this page: http://www.japan-guide.com/e/e2430.html
It gives the time it takes to Haneda from some of the major stations in Tokyo, i.e. Tokyo Station (30 minutes, 1 transfer), Shinjuku Station (45 minutes, 1 transfer), etc. So depending on where you stay, you'll want to check the time and make sure to leave a bit extra for leeway.