Maintenance and safety of cast iron skillet

I come from Stack Overflow and this it my first post on this branch of Stack Exchange!

I write here because I received a small skillet as a gift (I assume its material to be cast iron), and I don't know how to handle and maintain it properly because I have never used one. Also, I have a couple concerns regarding it and I hope that I could get proper advice here.

TL;DR (yes, this question in quite long, if you read it all I'd really appreciate)

Is it normal for the skillet to have residue when I pass my finger on it? Is it safe to cook in it? Out of the many advice that I could find on the Internet on how to clean it, which one(s) should I follow?

Detailed version

The skillet serves to keep food hot on the table by lighting a candle underneath it. I first saw it at a Japanese restaurant and I liked it a lot, the one that I have should come from the same place the restaurant bought it from.

Some pictures:

The first picture is of the stand: the candle is put in the hole, and the skillet is put above. The second pictures is of the handles, and the third is obviously of the skillet.

The person who gave it to me washed everything twice thouroughly. I think this might have caused some of the coating to come off from stand & handles, as you can see from the pictures. I wouldn't care for that, I also think that the material used for the stand is not iron as it is very light. I'll just use the stand and never wash it.

I noticed that the skillet itself, though, leaves a bit of residue when i rub my finger on its bottom. It's different from the pieces of coating that come off from the stand, it's a very fine powder. I've looked online, and it seems that from now on I'd better not wash it with water and clean it in other ways instead. The problem is that I've seen a lot of different advices on the Internet, and I can't figure out how to properly take care of the skillet. So here is my list of questions:

1) Is the residue normal? Can I get rid of it? Is it dangerous for my health to put food in the skillet?

2) Out of the many methods that I found to clean the skillet, which one should I use? I've seen people suggesting that I rub it with salt, then I apply a thin film of vegetable oil. Others say that it can be cleaned by pouring water in it while it is on the stove, and letting it evaporate.

3) While I don't care about the base, I'm not OK that the handles lose coating above my food. Should I avoid using them, or again there is something that I can do to stop it from coming off? If they are made of iron like the skillet, can I assume that a proper handling (e.g. scrubbing with salt, no more water, rubbing with oil) will work?

Thanks in advance.