Arashiyama from Osaka

My itinerary as below
31/5 to 5/6 Osaka
5/6 tp 7/6 Kyoto

Have few questions
1. Plan to go Arashiyama on 5th after arrive Kyoto, what is the Fastest way to travel?
2. Shall we check in hotel (Karaksa hotel at Omiya) or go straight to Arashiyama, (we have 3 cabin size luggage)
3. If go hotel first. How to travel from Omiya, is it convenient to take Keifuku Railways (Randen) from Omiya?
4. What is the best or safe time slot to book the Sagano Scenic Railway

1. Plan to go Arashiyama on 5th after arrive Kyoto, what is the Fastest way to travel?

If you will start at Umeda (JR-Osaka, Hankyu Umeda area), fastest way is by JR, from Osaka to Kyoto and then to Saga-Arashiyama.

2. Shall we check in hotel (Karaksa hotel at Omiya) or go straight to Arashiyama, (we have 3 cabin size luggage)

You can leave your luggage at Arashiyama, but it will take some time and money. I think you would better check in Karakusa hotel first and then take Keifuku.

3. If go hotel first. How to travel from Omiya, is it convenient to take Keifuku Railways (Randen) from Omiya?

Yes.

4. What is the best or safe time slot to book the Sagano Scenic Railway

I might misunderstand your question, but if you want to reserve the Sagano Scenic Railway, do it as early as possible at JR's ticket counter or some tourist agencies. You can check the availability here.

https://www.sagano-kanko.co.jp/en/kuseki.php#selectday

Both the JR option and Hankyu option Osaka to Saga-Arashiyama via Kyoto and Umeda to Hankyu Arashiyama take 50 minutes.

Except the Hankyu option is 400 yen, versus the JR option of 970 yen.

but if you wanna go to you hotel in Omiya and drop your bags off first, then JR to Kyoto, subway to Omiya. then Keifuku "Randen" to Arashiyama.

Best way to secure a seat on the Sagano railway is to reserve one at the Kansai region JR station. JR does the advanced tickets, the the Sagano Railway only sells tickets for the current day.

Both the JR option and Hankyu option Osaka to Saga-Arashiyama via Kyoto and Umeda to Hankyu Arashiyama take 50 minutes.

Except the Hankyu option is 400 yen, versus the JR option of 970 yen.

Yes, you are right. I underestimated the time for Kyoto to Saga-Arashiyama.

but if you wanna go to you hotel in Omiya and drop your bags off first, then JR to Kyoto, subway to Omiya. then Keifuku "Randen" to Arashiyama.

For Omiya, it might be better to take Hankyu. Omiya station is Hankyu line so you need to transfer twice if you take JR (JR to subway to Hankyu). If you take Hankyu, transfer at Katsura from limited express to semi-express (limited express does not stop at Omiya).