Exit from Higashi-Umeda Station

I'll be going to Kyoto but I'll be coming from Minamimorimachi Station. I know that I need to get off from Higashi Umeda and then walk to Umeda Station. Do you know what's the fastest/nearest exit # I should go to so I can reach JR Osaka Station?

Also when I reach JR Osaka, which is more time efficient queuing at the window to book 9 tickets to Kyoto? or queuing to buy the tickets at the machine, and trying to understand :)

Thank you.

You won't have to exit. The stations are all interconnected underground. Simply follow the bilingual signs towards JR Osaka Station.

Boarding towards the front of the train at Minamimorimachi will reduce walking distance just a little bit.

Also when I reach JR Osaka, which is more time efficient queuing at the window to book 9 tickets to Kyoto? or queuing to buy the tickets at the machine, and trying to understand :)

Don't you use prepaid cards? Icoca cards can be used on Osaka subway lines and the trains between Osaka and Kyoto and many other means of transportation around Kyoto and Osaka.

If not, then I recommend to use the ticket machine. The one way fare by JR from Osaka to Kyoto is 540 yen, and the machines are easy to use.

Do you know what's the fastest/nearest exit # I should go to so I can reach JR Osaka Station?

You will logically exit subway in Higashi-Umeda Station, but will still walk under the ground until around Umeda Station.
I guess you can easily make this transfer to Osaka Station in 10 minutes or so even without advance explanation like the following.

Higashi-Umeda Station
- http://www.kotsu.city.osaka.lg.jp/station-guide/T/t20/pdf/station.pdf
Trains from Minamimorimachi arrive to Track 2.
You will go upstairs from the northwest end of the platform, exit subway through nearby Northwest Gate, turn left and walk via a slope (marked on the map with #1 on orange background in a circle) onto Umeda underground mall.

Inside the mall you will just follow signs showing the direction of Umeda Station / JR Osaka station.
Getting around Umeda Station, you will find an escalator for JR Osaka Station.
Special Rapids running for Kyoto depart from Tracks 7 - 10.

Also when I reach JR Osaka, which is more time efficient queuing at the window to book 9 tickets to Kyoto? or queuing to buy the tickets at the machine, and trying to understand :)

Major JR stations are equipped with Japanese & English bilingual ticket-vending machines.
You can purchase probably 4 or 5 tickets at once from a machine.
If you have not got an IC transportation card, you might hope to get an ICOCA Card from a ticket-vending machine with an ICOCA logo.
Make sure that a passenger should use the same IC transportation card in entering and exiting the rail.
- http://www.jr-odekake.net/en/icoca-haruka/pdf/ICOCA_en.pdf