Chain and derailleur question I inherited a Motobecane Nomade with no derailleur. I am trying to replace the missing derailleur and chain. I was given a Shimano SIS Tourney rear derailleur long cage and front derailleur and shifters that I was like to mount on the bike.

Two questions:

Is that derailler feasible for this bike?

I have a PC 1051 10 speed chain. Will that work or can I use a KMC X8.93 6 7 8-speed chain or is some other chain is needed. If so what?
It depends on the rear wheel you are using. Specifically how many gears. Also you need to make sure your shifters (if they are indexed aka have a 'click' for eachgear change and are not infinitely adjustable ) match the amount of cogs on your casette/freewheel on the rear wheel.

If you are using non indexed/friction shifting you can use these shifters with any number of gears in the back (In my experience).

In my experience 9 speed chains can be used with 6-8 speed casette and also work alright on 10speed. Have not tested it for 11 speed. So in general if your chain isn't too wide (it doesn't rub against the neighbouring cogs of the casette/freewheel and it isn't too narrow (the chain easily and fully seats on the cog teeth without having to force it on) you should be fine.

In my experience and according to Sheldon Brown Shimano rear derailleurs can be used interchangeably with other speed rated Shimano rear derailleurs. So a 7s rear derailleurs can be used for 10 speed casette when using the correct shifter. Do make sure the chain properly fits the casette's chain guide wheels. In some cases you might have to install longer limit adjustment screws in the rear derailleurs to be able to properly adjust it but in most cases you won't.

So to answer your question: yes that derailleurs should work as long as you use a friction shifter or a properly matched (same number of speeds as your casette/freewheel) indexed shifter.

Sheldon Brown: https://www.sheldonbrown.com/speeds.html
More complex explanation: https://www.sheldonbrown.com/derailleur.html