How does the halving work when the number gets really small?
Eventually the reward will go from 0.00000001 BTC to zero and no more bitcoins will be created.
The block reward calculation is done as a right bitwise shift of a 64-bit signed integer, which means it is divided by two and rounded down. The integer is equal to the value in BTC * 100,000,000 since internally in the reference client software, all Bitcoin balances and values are stored as unsigned integers.
With an initial block reward of 50 BTC, it will take many 4-year periods for the block reward to reach zero.
How long will it take to generate all the coins?
The last block that will generate coins will be block #6,929,999 which should be generated at or near the year 2140. The total number of coins in circulation will then remain static at 20,999,999.9769 BTC.
Even if the allowed precision is expanded from the current 8 decimals, the total BTC in circulation will always be slightly below 21 million (assuming everything else stays the same). For example, with 16 decimals of precision, the end total would be 20,999,999.999999999496 BTC.
