Yes, the cord and controller from your Featherweight will work. Many Singers used the same 3 pin connector cord/button controller set up. I have several Singers and when I pull one out to use it I just grab the first cord/controller set I can reach. I've done it so many times that I couldn't begin to tell you which one actually came with which machine.
Tri Flow oil yes. If your machine is a 201-2 with the potted motor then you'll only want to use Tri Flow grease on the gear underneath the machine, not in the motor grease tubes. For those, you'll want to use Singer lube or just plain vaseline.
Welcome and congrats on getting your 201. I'm not a Singer gal but my 201 is my second favorite of all my 40+ machines.
Cari