I am using bitcoin core on windows 7, it takes forever to sync and during this time I cannot see any sending/receiving addresses in my
interface, I only see "balances" (empty), "recent transactions" (also empty).
Will addresses show up only after it is done syncing ?
a bit off-topic: Is it safe to just copy/paste the wallet.dat around or is it any risk if the sync is at a certain state while I
copy/paste the wallet to/from the bitcoin data folder ?
In Bitcoin Core, the "sending addresses" window is just an address book. If someone tells you an address to send bitcoins to them, and they want you to re-use that address in the future, then you can add that person's address to the address book along with a label so you can find it easily the next time you want to send them more bitcoins. If you haven't added any addresses to that address book, then obviously there aren't any to show you yet.
Bitcoin Core assumes that you will use bitcoin properly and generate a new address every time someone is going to send you bitcoins. It also generates a new address every time that you send a transaction so that it can be used to receive the change in your transaction back into your wallet. It mostly keeps all these addresses hidden from you. Anytime you need to give someone an address, you just click the "request payment" button. It will generate a brand new address for you to use, and show you that address. You can see the history of addresses that you have generated in the "receiving addresses" window, but if you haven't generated any yet, then there aren't any to see.
There is a "Backup Wallet" option under the "File" menu. If you want to copy your wallet.dat while the program is running, it would be best to use that "Backup Wallet". Otherwise, I would shut down Bitcoin Core before copying the file. You can shut it down while it is still synchronizing, it will pick up where it left off the next time you start it up.