a) Is this a common practice? Having one wallet online and another one locally?
Absolutely. It's a common practice with any type of money, not just bitcoin.
I have some of my U.S. currency in my "wallet" in my pocket. I have more of my U.S. currency stored securely in my home. I have even more of my U.S. currency on deposit at a federally insured institution (known as a "bank"). I have more of my U.S. currency invested in financial instruments that grow in value over time for use in retirement.
Why wouldn't you do something similar with your bitcoins?
Have a small amount in a mobile wallet on your smartphone for easy use anywhere. Have a larger amount stored in an online wallet that can be used to reload the phone and for larger purchases. Have an even larger amount stored securely at home and securely backed up offsite.
b) Is it easy to transfer money from the online wallet to the local one and vice versa?
Yes.
And does it cost?
Yes.
The amount it costs depends on how you received the bitcoins and how high the global transaction volume is at the time you want to send the transaction.
In general, you can expect to spend between 0.00005 BTC (0.05 mBTC) and 0.0003 BTC (0.30 mBTC) per transaction to send bitcoins from one wallet to the other.
c) What solution would you suggest for me? And which wallets?
Armory and Bitcoin Core will require you to run a full node and expend the necessary resources to do so. That means synchronizing the entire 100GB blockchain onto your computer and verifying every transaction that has ever been confirmed. This can take a while and will use a significant amount of internet bandwidth and storage space.
Other good options if you don't want to expend those resources are MultiBit and Electrum.
As for mobile wallets, I like Mycellium.
The only "online wallet" I've used is blockchain.info. They are buggy and can be frustrating at times, but for small amounts can be very convenient.
Depending on what country you are located in, you could also consider using an online service such as Coinbase or Circle. They both provide smartphone apps.
I hope my questions are not too naïve or tiresome.
Not at all.