Haruku / Icoca JR return ticket

I looked up the train schedule on hyperdia from Kyoto Station to Kansai Airport and found a JR Limited Express train I would like to take using my return ticket. It gives me the option of paying for a reserved seat or a unreserved seat fee. Will I need to pay any more using my Haruku return ticket? Also, do you know how many seats or passenger cars they set aside for unreserved seats.

From the Japan Guide page on this ticket package:
The ticket can be used on non-reserved seats on the JR Haruka limited express train from Kansai Airport to Osaka or Kyoto.

No idea how many carriages are non-reserved though. I suspect it would depend on the time of day and how many flights are expected to arrive. It's not too long a trip though, so you could probably get away with standing if the train's crowded and you're not too tired from the flight!

Woops, sorry, just realised you were travelling from Kyoto, not Osaka! It's an hour and a half, so you'll probably want a seat! I'd say reserve a seat if you're worried, or just get to the station a few minutes early so you can line up and be first on the train. You could always sit on your suitcase if there are no seats!

Thank you Sq. I will get in line early to sit in the unreserved section. I'm assuming with the Haruku return ticket everything will be prepaid in this section.Right ?
Do you know if I just show this pass to the gate agent or do I swipe this pass at the ticket gate?

Will I need to pay any more using my Haruka return ticket?

You are asking about an airport-bound ticket in a roundtrip ICOCA & HARUKA package, right?
When you do not use a reserved seat, you can take a JR Ltd. Express "Haruka" (not "Haruku") train to Kansai-airport Station just with this ticket (unless it is expired).
When you use a reserved seat, this ticket can cover the basic fare only, so a Ltd. Express charge for a reserved-seat ride (1290 to 1690 yen for Ordinary Class, depending on days) is required.

Do you know if I just show this pass to the gate agent or do I swipe this pass at the ticket gate?

Well, from this image, a ticket in this package seems to be a typical larger-sized magnetic-paper ticket, which you can put into a gate machine via a slot.
http://www.westjr.co.jp/global/en/travel-information/pass/icoca-haruka...
If you have reserved your seat, you can put this ticket and the reserved-seat ticket together into a gate machine.
Please make sure to use a JR-West gate (e.g. Central Gate) in Kyoto Station.
(The Shinkansen zone of Kyoto Station is managed by JR-Central.)

how many seats or passenger cars they set aside for unreserved seats.

That depends on trains. Roughly speaking, 2 or 3 cars of 6 or 9 cars of a "Haruka" train are for passengers without seat reservation.

One or two "Haruka" trains run per hour in each direction. Unless you travel during a busy time or stick to one or a few specific trains, usually you have a chance to secure a seat, hopefully without reservation.

A JR Ltd. Express "Haruka" train is in either 6 or 9 cars. Car No. 1 is always a higher-class car.
Concerning airport-bound "Haruka" trains, 2 or 3 cars (Cars Nos. 5 - 6 or Cars Nos. 4 - 6) are for passengers without seat reservation.

Ive taken the Haruka about 5 times.
Summer
Autumn
Winter
Never had to stand.

Great information Omotenashi ! Yes, I am traveling Airport Bound to KIX. My train leaves Kyoto at 1402 on a Friday afternoon. I hope this is not considered peak times. Having at least 2 cars for non reserved seating, I think I will not have a problem. This pass is a good deal knowing I can travel from kyoto to Kansai without changing trains with ALL my luggage. Thanks again !