I have been using Bitcoins since Jan 2014 and know enough about it but there's something I don't understand. Miners approve transactions. This is a fact.
That depends on what you mean when you say "approve". All peers on the network verify the transaction and will only relay it to the miners if it is valid, so miners aren't the only ones that verify transactions.
What miners to is "confirm transactions". This means that they add transactions to the blockchain to set the order of the transactions.
And there have been instances with me where I have not included fees for a large transaction and it got reversed.
So, you've finally learned to always include a transaction fee with your transactions?
Suppose, I buy a few mining rigs and start mining at some pool, so I am a miner now, so does that mean I can approve some txns and reject some on my wish ??
That depends on the pool you choose. In most pools, the pool operator gets to choose the transactions that get confirmed. There are some pools (such as p2pool) where the members get to choose which transactions to confirm, but you'll only get to choose for the blocks that you solve. How often that will happen will depend on how much hashing power you have, and what the current difficulty is.
At the current difficulty of 39457671307.1 you'll need approximately 1962 terahash per second if you want to be able to solve one block per day.
With 280 terahash per second, you'll be able to solve approximately one block per week. (at least for the first week, after that difficulty will change every 2 weeks).
With 64.5 terahash per second, you'll be able to solve approximately one block per month. (except that difficulty will change by then, so it is likely to actually take longer).
With 5.375 terahash per second, you'd be able to solve approximately one block per year. (except that difficulty will change quite a bit by then, so it is likely to take significantly longer).
With 537.5 gigahash per second, you'd be able to solve approximately one block per decade. (except that difficulty will change a lot by then, so it is possible that you will never solve a block).
With 537.5 megahash per second, you'd be able to solve approximately one block per century. (except that difficulty will be completely different by then, so it is likely that you'll never solve a block).
