Definitely 30s drums. Cool that you have a picture of your grandfather with them.
The dog leg bass drum mounted arm is a Slingerland number 766 and is missing the clamp arm and screw.
The Snare is a Ludwig Standard. Since you don't show the strainer, it's hard to pinpoint the date. Could be as early as 1935.
The bass drum is a Ludwig Artist's model Bass drum in what I believe is Abalone Pearl.
The bass drum pedal is the Ludwig Original model.
The hi hat stand is a Walberg and Auge 804.
The item on top of the bass drum on the left is a clamp on spur. There should be two of them. The Muffler on the right with the two large round pads is probably a Walberg and Auge. Could also be Ludwig or Slingerland, which were usually made by Walberg and Auge. If they are they will usually be stamped with their name. If no name stamped then probably W & A.
The two black plastic parts, the rubber washer and the drum key are modern parts and not correct for the set. The drum key might be old but looks like some generic ones that used to be common not that long ago. Should work fine though.
The cymbals could be from any number of makers, but could be Zildjian. They should have some sort of writing and logo stamped on them.
Ebay or Reverb is probably the best source of parts to get the cymbal arm parts.
There is a seller on ebay, biggerspeck4tao who has lots of vintage parts and usually very fair prices. His store on ebay is called Mad Scientist Drums
The hi hat is missing a couple of felt washers, a cupped cymbal washer, a large wing nut in 1/4-20 thread and the clutch.
This is the clutch that you need.
https://www.ebay.com/itm/187370026920
As far as cleaning them. Be very careful with the Abalone Pearl wrap as it looks quite fragile. Personally, I would just use a damp cloth to get any surfact dust off. They look like they have been stored in cases and have a very nice patina.
