Osaka airport transfers

My questions:
1. How far is Osaka airport from Shin Osaka Esaka Tokyu REI hotel?
2. What is the best option to reach the airport from this hotel -- bus, taxi , train?
3. Have to take a flight to Bangkok on a Friday at 11.45 am. So will I encounter any peak or rush hour traffic or rush? I guess I will have to start from the hotel at least by 7 am?

Do you mean Osaka Itami airport or Kansai International airport?

According to the hotelfs website -

g1 minute on foot from Esaka Station on the Midosuji Subway Line (4 minutes by Subway from Shin-osaka Station, 11 minutes by Subway from Umeda Station)

26 minutes by train from Osaka (Itami) Airport to Esaka Stationh

Take the train and the subway.

I have to reach Kansai airport.

Take the Haruka Express to/from Shin-Osaka and then the subway, as explained in the hotel instructions. The Haruka Express runs 30 times / day.

http://www.hyperdia.com/cgi/en/search.html?dep_node=KANSAI%20AIRPORT&a...

http://www.hyperdia.com/cgi/en/intervaltime.html?dep_node=KANSAI%20AIR...

Please note, "Haruka Express" does not exist; the name is just "Haruka", and it is a limited express service.

In terms of getting from your hotel to KIX.

Hyperdia actually recommends you take the subway from Esaka down to Tennoji and change there for a Haruka, but I would think getting off at Shin-Osaka makes more sense. The subway between Esaka and Shin-Osaka might be busy, but the Haruka is unlikely to be since it is mostly used by people going to the airport vs. commuters. There is an 8:17 Haruka that runs from Shin-Osaka to KIX arriving at 9:13. If you want to be extra careful there is a 7:47 that arrives in KIX a little before 9:00. If you leave Esaka subway station at 7:52, you will be in Shin-Osaka before 8:00 giving you close to 20 minutes to make the transfer. If you want the earlier 7:47 Haruka then take a subway from Esaka station at 7:28 and you will be in Shin-Osaka by 7:32 giving you a nice 15 minute cushion to make your train. By the time you are leaving you will have a good idea of how long it takes you to walk from your hotel to Esaka Station since you'll probably be doing it every day of your visit.

Unless you have a lot of travel outside of Osaka you've not mentioned I would think this ticket makes the most sense:
http://www.westjr.co.jp/global/en/ticket/icoca-haruka/

You can pay 4600 yen and it will cover your round trip to KIX from Shin-Osaka and give you an IC card to use for the subways you will be using pre-loaded with 1500 yen and include the refundable 500 yen for having the card.

Good luck!

Thank you so much.