Hi,
No personal experience but here are my 2 cents.
The recent decision of Ukraine to close land borders with Russia hasn't affected railway borders which continue to be open.
Unfortunately the only direct train between Nikolaev and Simferopol leaves at the ungodly hour of 04:38, but at least it means you arrive to Simferopol at 11:25 giving you plenty of time to continue to Feodosia.
You can book the ticket easily online if you follow these instructions:
http://www.seat61.com/Ukraine.htm#How_to_buy_Ukrainian_train_tickets
I think the trains from Ukraine to the Krim are probably not very busy since the secession, so you might leave buying the ticket until you get to Nikolaev.
Your passport and Russian visa will be checked when you enter the Crimea. There are no issues continuing to Moscow by either train or plane. You don't need a double entry visa, but it doen't hurt if you already have one.
Best way to book Russian train tickets is from Russian Railways website, but again since the summer season is over I think you'll have no problem buying the ticket at the station.
The railway between Rostov and Moscow(taken by the trains to the Crimea since the unification) is briefly passing through Ukrainian territory, but this never was a problem, not even during the hottest times of the war in the Donbass, it is relatively far from that anyway.
I just checked the RZHD website and it looks like there are either no dierct train from the Crimea to Moscow or you can't book them online for some reason. There are however plenty of trains from Feodosia(coming from Sevastopol) to Krasnodar via the train ferry over the Kerch Strait.
NB: Having no exit stamp from Ukraine might give you trouble if you want to enter Ukraine later using the same passport!