Do I have to buy a full bitcoin to get the price increase? If I buy half a bitcoin at $500 and the value of a bitcoin goes up to $1000, does that mean I earn 1 bitcoin or do I have to buy a full bitcoin to get the price increase? How does it work? Please give me some examples.
If you have 0.1 BTC and the Bitcoin price is $10,000, it is worth $1000. 
If the Bitcoin price becomes $20,000 you will still have 0.1 BTC but it will be worth $2000.