Hi meirK,
That's an ambitious list for 2.5 days, but yes I think it can be done. It'd be quite hard work, involving a lot of trains and walking around, so it depends how you like to do things. If you really want to cover all that, I'd suggest the following:
April 9th go to Nara. If you arrive Kyoto at 11am, drop your stuff off and head straight to Nara, you can spend the afternoon there. That's enough time to visit Todaiji (home of the Great Buddha) and nearby Kofukuji; of course there's a lot more to Nara than just those two temples, but those are the main draws and should be satisfying enough. In the evening, you could visit Gion and Maruyama Park when you get back to Kyoto (Maruyama will be both beautiful and lively with all the cherry blossom parties going on)
April 10th cover all the temples and shrines you've listed on the east side of the city; from north to south, that would mean starting with the Philosopher's Path (walk it from Ginkakuji to Nanzenji - two temples not on your list, but natural to include with Philosophers Path and both well worth visiting), and also visit the Keage Incline (amazing cherry blossom spot near Nanzenji) while you're at it, and perhaps also Heian Shrine. Then head down to Kiyomizu temple, and finish at Fushimi Inari. You can use the Keihan line for this day, it'd be a big day with lots of walking but I've basically done more or less exactly that in the past. Best to go from north to south as Fushimi Inari is open 24hrs (and well lit at night) so you don't have to worry about rushing to get there. It's very cool at night too (though less good for photos obviously)
April 11th head to Kinkakuji then Arashiyama, both on the west of the city; Arashiyama is a whole district and needs a good chunk of time, so that's do for the day, but you could try to visit Nishiki market beforehand.
So, that covers everything, and is doable if you're happy to be constantly on the move on trains and buses and on foot. Do bear in mind that you'll be hitting Kyoto at full bloom for the cherry blossoms (lucky you!) which means lots of crowds at most of these places; you may want to consider slowing the pace a little and visiting some nice cherry blossom spots, maybe walking along the Kamo river etc, here's a list of the best ones:
http://www.4corners7seas.com/cherry-blossoms-kyoto/If you leave one thing off your list, I'd say Nishiki market... or you could free up a big chunk of time by leaving out either Nara or Arashiyama (I think if you end up really pressed for time, I'd say omit Arashiyama). It really depends how you like to travel, pack in as much as possible vs take your time to enjoy it, and so on.
Anyway, hope this helps!