My questions:
a) Is this a common practice? Having one wallet online and another one locally?
b) Is it easy to transfer money from the online wallet to the local one and vice versa? And does it cost?
c) What solution would you suggest for me? And which wallets?
a) Yes. Others have multiple wallets too with lots of associated addresses.
b) Yes as it was the main good thing when using bitcoin. Cost vary or should I say transaction fees.
c) You already mentioned it : "I’d feel safer if I have my bitcoins locally, on my computer (with backup, I suppose). So, my idea is to have a local desktop wallet (like Armory or Bitcoin Core) and one online (preferably one that’s been up for quite a long time) in order to buy and sell, eventually, or even pay for something."