Yes, a lot of people did that, it much make sense if your stay is in kyoto.

Not sure on different station, but no difference between buying single and return ticket. so you can just buy your single ticket back to KIX once you reach there.

Its the same thing. Haruka tickets starts from 1.1k yen, then you just add on 2k yen for the icoca card itself, which consists of 1.5k yen credit and 500 yen deposit, which can be claimed back once you return the ICOCA card.
Just think it like addon, but the addon is no difference with buying them separately.
Note:
You are not purchasing the ticket through online payment. For haruka case, you are just plainly reserve the ticket. I think the only main point about the reservation is to make sure supply of ICOCA card is sufficient there.
You still have to go to their office in KIX once you arrived to make your payment and get the ticket with ICOCA card.
Better just go there and buy the ticket itself better.

You can choose either buy single or return ticket, but return ticket only valid for 14 days.
All you need to do is just tell the receptionist the station you are going and the station that you will be taking on your departure day. They will do the calculation and give you the ticket.
Same here, single and return ticket price is the SAME, so no difference between buying single ticket and return ticket. The only difference is that you have to go to certain station to buy haruka ticket if you bought only the single ticket, but you are not bound to 14 days validity period.

All their service counter are listed under the website itself, you can buy the ticket anytime from these counter, but passport have to be presented when buying.

This is their website.
https://www.westjr.co.jp/global/en/ticket/icoca-haruka/

Just came back from Kansai Region. Arashiyama is big man. I don't know how much you want to explore, but it definitely took me a day in Arashiyama.

Is possible, went there last march to Arashiyama for half a day ( until after lunch ) then continue to explore Kinkakuji, if not possible just schedule another visit later on. I will be going to Osaka/Kyoto again during mid of Nov this year 

I went to these places:

* Arashiyama Bamboo Grove (spent roughly 1 hour)

* Arashiyama Monkey Park (spent 1.3h)

* Tenryuji Temple (spent 1-2h)

*Otagi Nenbutsuji Temple (Recommended!) (spent 1.3h)

The thing is, getting around these areas required some walking. Had to go back in the evening to catch dinner.

TIPS: Wake up early and explore more.