Are suit cases allowed in JR east lines?

Yes
Yes
Yes

There's no prohibition on suitcases, but I'd be careful about your timing. If you arrive in the late afternoon, you will probably be heading into Tokyo while the commuters are all leaving, so the initial ride should be no problem. However, it could just be very difficult to squeeze in with so much luggage at a busy time.
However, once you get out of the city, things should be easier.

So, suitcases are allowed, but just be conscious of the timing so you aren't stuck in very packed commuter routes.

Yes, you can. If you get the JR railway from Narita, there is not directly to Kurihama.
You need to change the express train from Shinagawa or Yokohama then to Kurihama.
So it is not easy carrying bulk luggage to transfer from one platform to another.
Hope it will help.

Suitcases are allowed on all trains, including those run by JR East. However, Bringing 2 of those large-size suitcases will be a hindrance to your travel. There are lockers in train stations, but none that would fit such suitcases.
Also, the space for such suitcases is limited on the Shinkansen. There is only enough room for 2 of such cases at the end of each car. Before I knew better, the first time I went to Japan I took a medium-size suitcase plus a backpack on wheels. I found that I did not need all the stuff I had packed in this larger suitcase. Now I only take the backpack and pack an empty foldable backpack inside it.

I would think that trains running from Narita Airport would allow suitcases -- since most people using those trains are people who just flew into Narita from somewhere.

I've only taken buses (not trains) from Narita. The buses have storage bays underneath for big luggage.

I'm pretty sure the trains also have storage areas for suitcases, at the ends of the cars. Don't worry about anything being stolen -- it just doesn't happen in Japan!
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