These are my questions:
After the airdrop a new private key will show up in my ETH Jaxx wallet?
Will I have to export my private keys to a different wallet that supports DimonCoin?
Which wallet should I used so I can see and use the Dimoncoins that will be airdroped?
Regards
Your privatekey needs to remain private, don't EVER share it online. Buy a hardware wallet (Ledger nano 75 bucks) and learn to use that.
You NEVER NEVER NEVER 'export' private keys anywhere. Anyone asking you for your private key is going to rob you blind.
Use myetherwallet.com for the time being. Make sure you got the right site because there are many spoofs out there.
This is the correct one:

EDIT: I don't know jaxx but if it generates a JSON file, you can use that file to 'import' your address on myetherwallet and acces the funds connected to that address on myetherwallet. Not sure though since I dont use Jaxx.