Hi Prem,
There are a number of questions that pop up and are making me scratch my head. But to answer your questions in the order you asked them...
Regarding the free hotel transfer from Itami Airport, if the hotel is providing you a free ride, they are in charge of it and I am not in a position to say if their schedule is accurate or not. There is no reason to believe it wouldn't be though.
About getting around Osaka, as you can see on the Westin Westin website you are almost next door to the Umeda Sky Bldg. To go to the Abeno Harukas Bldg, it is too far to walk from your hotel, but very easy to reach by train or subway, and it is literally across the street from Tennoji Station. There are several rail companies you can take, but since you are going to use a JR Pass, you can go to JR Osaka Stn. (see the Westin website map again) and take the loop line to Tennoji. I believe the last time you can go enter the observation deck is 9:30 PM, so be there earlier. If possible, just before sunset is ideal to watch the city change from day to night.
For Dotonbori, from Osaka or Umeda Stn. take the Midosuji subway (you need to pay 240 yen; this is not covered by the Pass) to Namba Stn. and from there it's only a few minutes on foot. It is much, much better at night. I recommend that you go to each place after you see Kyoto and Nara, which would free up Day 4. You could see more of Kyoto or take half a day and go see Himeji and Kokoen Garden, which has Japan's finest castle. You can get there fast by bullet train and add to your savings.
What I find surprising is that you chose a hotel by Narita airport. For your last night it might make sense (but not really, if you want to spend your last morning in Japan seeing Tokyo), but as you already mentioned it is about an hour by train outside of Tokyo and about 60 kilometers away. You can use your JR Pass on the Narita Express for the round trip each day (and maybe even recoup the cost of the JR Pass) but it is an unnecessary waste of two hours of each day. Is there no other closer place in Tokyo you could stay at?
If your departure out of Japan is at 7:35 PM, then you should be at the airport between 5 and 5:30PM at the latest. The transport takes about an hour, so you could stay in Tokyo until 4 to 4:30 or so. There is a cheap 1000 yen bus you can take, but if you want to play it safe and avoid any possible traffic problem, then you could use a Keisei Skyliner Discount Ticket from Ueno Station.
Getting around Tokyo, Osaka etc is quite easy and it is more convenient just doing it yourself without paying for some tour.
I have never met anyone who found the regular bullet train seats to be uncomfortable or unsatisfactory. To me it is not necessary to pay more for the Green Seats. But if you want a bit wider seats etc, you certainly can pay the extra fee for it.
As to what to see in each place, a lot depends on your interests of course. For Kyoto the big 3 places to see are
Kinkakuji, Kiyomizudera and the Fushimi Inari Shrine. Kinkakuji you can see in 45 minutes, tops. Kiyomizudera you can be through in about 90 minutes leisurely. Fushimi Inari could take a couple of hours to all day if you want to romp over every trail. There is more than enough around each place to fill up an entire day. Other places you can look through are the Higashi and Nishi Honganji temples (near Kyoto Station and free), Toji Temple and Sanjusangendo (both near Kyoto Stn. too).
For Nara, the best is all in or near Nara Park, about 20 minutes on foot from the JR Nara Stn. The Todaiji Temple is a must-see place. Also feed the deer around it and don't miss the Kofukuji Temple and Kasuga Shrine. Also close by are the Isuien and Yoshikien Gardens, which most people storm past and don't even notice.
For Tokyo, you can use your JR Pass on the Yamanote Line which stops at numerous popular places for tourists, so it can be quite helpful if you still have time left on your Pass. One of the most popular places to see in Tokyo is the Sensoji Temple. Harajuku on a Sunday afternoon is also amazing to see the youth their in wild fashions, and the walk through Meiji Shrine and Yoyogi Park next to it is quite relaxing. The Sky Tree is very pricey but has the best view over the whole city - it is close to the Sensoji Temple. There are countless places to go: Shinjuku and Shibuya for shopping, and at night for the endless lights and neon, Odaiba at night for a real adventure, Shinjuku Gyoen Park, Hamarikyu Gardens, Rikugien Garden, Ginza for the overpriced shopping, Kiyosumi Garden, Koishikawa Korakuen Garden, Roppongi for the ex-pat environment, Kappabashi for the mind blowing realistic plastic restaurant displays for sale, etc.
See the links I gave above for lots more ideas.
Good luck.
an example