13 days visiting Tokyo - Kyoto - Osaka

My friend and I will be traveling to Japan beginning of May for 13days. I've got a couple of questions I just wanted confirmation on before buying the passes I'm planning on buying as well as a question on train times.

1. We will be landing at Kansai airport and wish to travel straight from there to Tokyo (shin-osaka on the Haruka express and then Hikari shinkansen to Tokyo) we will be landing just after 5pm so will probably be catching the first train around 6pm. My question is when does the last Hikari train run from Shin-osaka to Tokyo? Just wondering if we will make it.

2. My plan was to purchase a 7day JR pass for when we're in Tokyo for 3days and to cover our shinkansen to Kyoto (just because to buy individual tickets whilst in Tokyo and the shinskansen came up to more than the cost of a 7day pass) and then a Kansai area pass for our couple of days in Kyoto and Osaka in the end. My reason for getting a Kansai pass and not the 14day JR pass is because as far as I could see on a map of Kyoto we will be staying in Nakagyo-ku area and traveling towards and around the North East & Gion area and I couldn't see any JR trains running in that area but a lot of other railway companies which is covered by the kansai pass if I'm not mistaken. Is this true? The only JR line I could see was at Kyoto station and from there heading North West and South East directions which didn't come close to the areas we'd be visiting.

3. Can I purchase my and my friends passes and hand her hers when we meet at the airport? This is due to the postal service being a lot more reliable in the UK than SA at the moment.

Thank you a lot in advance for the help.