Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

If finding a block is the result of mining,

It is.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

which is the process of transaction verification,

It is not. Mining is the process of transaction "confirmation", not transaction "verification". There is a difference. All nodes that properly implement the protocol perform verification on all transactions and all blocks. However, only the miner that successfully solves the block that has the transaction in it "confirms" the transaction.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

so what will happen when all the bitcoins are mined out? The reward for mining will be gone. So who is going to verify all the transactions?

Miners receive a block reward for their effort. Currently the block reward consists of the sum of a block subsidy of 25 brand new bitcoins PLUS the transaction fees for all transactions included in the block. Every 210,000 blocks (approximately every 4 years) the block subsidy is cut in half and rounded down to the nearest satoshi. This means that the block subsidy will get smaller over time. Meanwhile, as bitcoin becomes more popular, the total number of transactions (and total value of all transaction fees) should increase over time. Eventually (around the year 2140) when the block subsidy is 0, the block reward will consist of ONLY the transaction fees. Hopefully in the next 125 years bitcoin will become popular enough that the fees will be sufficient for mining to continue at a high enough level.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

will the bitcoin die when its all mined up?

It shouldn't.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

Even if that takes many many years,

Approximately 125 more years.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

will the halvings and difficulty skyrocketing effect the stability of bitcoin?

It shouldn't. It is designed to hopefully reach a balance.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

because it will eventually just become completely unworth it to mine,

That shouldn't be possible. If enough miners shut off their equipment, then the difficulty decreases (just like it has the past two adjustments). The decrease in difficulty makes mining more profitable for those that remain.

Quote from: stopthe_bomb on December 22, 2014, 08:13:10 PM

which would put the bitcoin at huge risk for the 51% takeover if I am right?

Yes, if enough people stop mining, then there is always a risk of one entity gaining permanent control of more than 50% of the total global hash power. However, I don't see any reason yet for such a significant number of miners to stop.