Is it possible to stop by in Amanohashidate?

Hello, so next December I'm going to Kinosaki Onsen for one night. On the next day, before going back to Kyoto, I'm planning to go to Amanohashidate.

My questions are:
1. Because I have a JR Pass, I read that I still have to pay a train from Fukuchiyama to Amanohashidate station because it's not covered by JR Pass. On Hyperdia I found out that I have only 7 minute transit from Fukuchiyama before taking the LTD. EXP HASHIDATE 1 train to Amanohashidate. Can I just get in on that train or I should buy another ticket with a risk that I'm not making it on that train? Because the next train is around 1 hour after and I think if I don't make it, it'll affect my itinerary for the whole day.

Anyway this is the train that I'm planning to take based on Hyperdia:
09:33 - 10:42 KINOSAKIONSEN - FUKUCHIYAMA (LTD. EXP KONOTORI 12)
---
10:49 - 11:25 FUKUCHIYAMA - AMANOHASHIDATE (LTD. EXP HASHIDATE 1) --OR--
11:54 - 12:33 FUKUCHIYAMA - AMANOHASHIDATE (LTD. EXP HASHIDATE 3)

2. Based on the first question, is it worth it and possible to actually stop by in Amanohashidate for a short time period, because I have to go to Kyoto in the evening?

Also based on Hyperdia, I'm planning to go to Kyoto on this train:
17:35 - 19:53 AMANOHASHIDATE - KYOTO (LTD. EXP HASHIDATE 8)

3. If it's possible to visit, should I get to the opposite side of Amanohashidate to visit Kasamatsu Park (I'm planning to use the sightseeing boat) or it's just possible to visit Amanohashidate View Land in the station side?

Thank you very much.