Transferring from Limited to Shinkansen

Hello! I just wanted to clarify something. This is about what ticket to insert at the ticket gates.

I have reserved tickets from Tsuruoka to Tokyo via Niigata.
I have three tickets atm:
One base fare ticket.
One supplementary ticket is for the limited ride from Tsuruoka to Niigata, and another for the Shinkansen transfer from Niigata to Tokyo.

1. Correct me if I'm wrong but, at Tsuruoka Station, since I'll be riding a limited train first, I should insert the base and limited supplementary ticket right?

2. At Niigata Station, once I go through the Shinkansen ticket gate, do I insert all three?

Thanks!

Normally insert all the tickets together, and the gate will keep the ones for the expired leg. If the gate objects - simply show at the manned gate.

1)
Yes, so.

2)
Basically, so, but you have to insert all at "transfer (tix) gate" if in short time.
http://www.jreast.co.jp/e/stations/e1137.html

If not, enough time, you can also out from conventional line's ticket gate without Shinkansn tix
for shopping, eating as break or short explore around the Niigata station.
In this case, only base fare tix will left, for re-entering go to Shinkansen ticket gate with left 2 tix.

And,
If you want a LtdExp tix to be collected at Niigata as a "souvenir",
if you declare it to the station staff by the gate, you can take it by they do "invalid" it.
The tix of Shinkanse is also same, no commission, try it if need.
If you want to use Japanese, remember this short phrase, no hard.
すみません、記念に欲しいので「無効印」を押して貰えませんか?
(Sumimasen, Kinen-ni Hoshii-node, "Mukou-inn" wo Oshite-morae-masenka?)
= I want it to commemorate, "invalid stamp" please.
(copy to below and click speaker icon to practice natural pronunciation)
http://voicetext.jp/
(micro ver. is just a bit smaller size as sound file.)
(速さ = speed may 80% may better at first)

I believe:
(1) You are correct. But upon exiting at the Niigata, the turnstile will collect the two tickets (unless you want to keep them as souvenirs, then exit thru the manned gate).

(2) At Niigata Shinkansen turnstile, insert just the Shinkansen ticket. Since you mentioned you have only one Shinkansen ticket, I am guessing it is a non-reserved seat ticket. When you arrive at Tokyo station, the exit turnstile will collect it.

When in doubt, just use the manned gate. They are generally very patient and helpful to tourists and you won't be holding up the locals while trying to figure out what to do at the automated gate.