Shinkansen conditions at this 2015 year end

I will go to Japan during this 2015 Year End with my family (4 persons). Please inform me shinkansen condition and your suggestion for our trips below :
Dec 28 Kyoto to Nagoya and Dec 30 Nagoya to Tokyo. Is it possible for us to get seats if we buy at KIX on Dec 26 when we arrive ?

Dec 31 Tokyo to Gala Yuzawa Ski Resort and Jan 2 NEX Tokyo to Narita. May I book these 2 trips thru JR East Online reservation ?

Thank you.

Hi
I use Shinkansen every month for business.
Especiall,year end is very very crowded it.

You can check this site.
http://www.jr.cyberstation.ne.jp/vacancy/Vacancy.html
However it is Japanese only,I show tips to use it.

1,After open this site,you can see 7white blank and blue botton.
2,First blamk is month and day(if you want 28 →12 and 28 choose)
3,Under it is departure time (you also choose)
4,Next long blank is name of shinkansen .(please choice second one :のぞみ・ひかり・みずほ・さくら・つばめ)
5,you can see new blank under it. it is station name.
6,you want to go to nagoya from kyoto right?
Please paste きょうと　left and なごや　in right box.
(it mean Kyoto to Nagoya)
7,and then click the right blue botton,it is seach.
8,you can crowded condition on Shinlansen.

if you have question,please contact skype:
milkcoffee505

Tokyo is とうきょう
（japanese hiragana charactor）

Dec 28 Kyoto to Nagoya

Not particularly crowded, especially before the evening. Also, it is a relatively short ride.

and Dec 30 Nagoya to Tokyo.

Somewhat crowded but not extreme. The situation is more extreme in the opposite direction.

Is it possible for us to get seats if we buy at KIX on Dec 26 when we arrive ?

I feel so, especially if you are flexible with the time of travel.

Dec 31 Tokyo to Gala Yuzawa Ski Resort

This could be rather crowded, especially in the mornings. Later in the evening, the trains will turn rather empty, though.

and Jan 2 NEX Tokyo to Narita.

Not particularly crowded. The rush is in the opposite direction.

May I book these 2 trips thru JR East Online reservation ?

Yes, the latter two trips can be booked online.

Thanks Micck and Uji for your information and suggestion.
I jus tried Micck's guidence, after click blue button (search) there was a new menu but I did not know what the mean but if I click the blue button in the (it seems a search button) I got a result with "O" and "*" mark. What the mean of this marked ? Could you inform me the meaning of these result ?
Thank you in advance for your help.
Arigatou gozaimasu.