I am a little confused here about the Online Reservations.

We will be using JR East to travel around Tohoku and Nagano:

(1) if we make reservations online for trains, can we collect the tickets only on the day of the train ride?

(2) if we have not collected the tickets but we cannot make it for that train we reserved (ie. late), will we be penalised?

(3) if we have the tickets but missed our train, can we re-book for another later train?

(4) alternatively, can we book our subsequent trains in Tohoku in JR stations in Tohoku or must we pre-book and collect tickets for all the trains we need throughout the stay?

If you are purchasing passes from outside Japan, you will be issued with a coupon to collect your tickets whenever you get into Japan.

However, rules for cancellation and refund vary depending on what type of ticket or pass you have.

I would suggest taking a good look at ticketing rules at their website to determine what the rules are for the particular ticket or pass you will be using.

Sorry, forgot to mention. We will be using JR East Pass.

One more question, we will be going to Nagano - Jigokudani Koen (Snow Monkey Park). Where can book the portion of the train from Nagano to Yudanaka (not covered by JR Pass)?

No, at any time when you are in possession of your JR East Pass. Read the website's terms of use carefully:
http://jreast-shinkansen-reservation.eki-net.com/PC/English/JRTicket/S...

if we have not collected the tickets but we cannot make it for that train we reserved (ie. late), will we be penalised?

Yes.

if we have the tickets but missed our train, can we re-book for another later train?

Yes.

alternatively, can we book our subsequent trains in Tohoku in JR stations in Tohoku or must we pre-book and collect tickets for all the trains we need throughout the stay?