I know, I already should know it by now,
However:
What happens when all bitcoins are mined?
Mining is import for the system. Who will do it after the situation? Who will spend the energy?
Over the course of the years, as the bitcoin economy grows, there will develop a premium on near-term transaction processing. People who desire to have their transactions processed quickly will pay a transaction fee over the average rate, in order to incentize miners to include that transaction over one with a lower or zero fee. Long before the last new bitcoin is created, the block reward will be so vanishingly small as to be insignificant. If the bitcoin economy isn't large enough by 2025 or so, it never will be. The last bitcoin won't be created until around 2130.
Is there a restriction to the "size" of the coins?
There is a common misconseption here, I think. A bitcoin is simply a unit, it doesn't actually exist even as a digital artifact; like an email or an mp3 file. There is only the transaction entries in the blockchain. The blockchain functions as a massive, collective ledger system. Amounts are deducted from an existing address in the blockchain and added to another (new or existing) address in the blockchain. There is a size limit on a block, but that is a agreed convention between miners who all use the 'conventional' codebase. That limit can be raised, or removed altogether. Standard clients have no size limitations on blocks or wallet.dat files.