Osaka-Himeji-Kobe

I'm planning to travel from Osaka to Himeji to Kobe then back to Osaka in one day. Here're my questions:
1. Is it possible to cover the main attractions in Himeji and Kobe in one day?
2. What is the cheapest way to go from Osaka to Himeji, then from Himeji to Kobe and back to Osaka from Kobe? Is there any discount pass pr something like that? I don't have a JR Pass
Thank you.

Is it possible to cover the main attractions in Himeji and Kobe in one day?

It depends on your travel pace. If you travel at a fast pace, you can pack in Himeji Castle and several of Kobe's main sights. But if you travel at a slow pace, you might have time for Himeji Castle and only one attraction in Kobe.

I have been to Himeji Castle with various friends. Some walked through in less than an hour. Others read every explanatory sign and spent several hours there.

For the average tourist, I recommend to spend three hours in Himeji, including transport between the station and the castle. That translates into: AM in Himeji - PM in Kobe.

Note also that a major renovation of Himeji Castle starts this autumn with scaffolding.

What is the cheapest way to go from Osaka to Himeji, then from Himeji to Kobe and back to Osaka from Kobe?

A 1-day JR West Kansai Pass costs 2000 yen and covers loval and rapid JR transportation only (shinkansen and Osaka and Kobe subways not included). By regular JR tickets, it would cost around 3000 yen. Even with cheaper non-JR transportation, regular tickets would cost over 2000 yen.

So, I recommend to use a JR West Kansai Pass:
http://www.japan-guide.com/e/e2361_03.html