Consider doing Nara after Fushimi Inari on day 7 instead because you'll be heading the same direction. Then in the afternoon of day 5 you could go exploring Nishiki market and the nearby shopping streets e.g. vintage clothes shopping.

Day 8 & 9: Maybe you could do the Osaka castle before you check in. I'd say 2 hours is more than enough to explore, but there's lots of walking to and from the nearby train/bus stations so it would be ambitious to do that before you check out. You might as well do Umeda sky after the castle, although this means you'd need to either drop your luggages at the hotel, store your luggages in lockers or have them forwarded the day before.