Is it normal not to see my sending/receiving addresses while the bitcoin client is syncing? 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 ?
1)

No.

Receiving addresses are not shown because they are intended to be used only for a single payment. The practice of reusing addresses weakens your privacy, but also that of others in the system who you interact with.

It is possible to see the receive addresses that were created in the past, but you need to explicitly check the address reuse box in the receive payment tab.

2)

You can move the wallet.dat file when Bitcoin Core is not running. You can also copy to make a backup, but realize that the backup will need to be recreated every 100 incoming payments (this will change in 0.13, where a backup will be permanently valid). Do not actually use copies of a wallet from multiple locations at once.