Yes. Mining supports the network. Eventually the reward for mining will be just the transaction fees.

That would depend on the number of transactions in a block that a miner solves.  The current transaction fee is 0.005 BTC I believe.

By then transaction fees will most likely be higher. If there are too many transactions not all of them will get mine into the blockchain immediately. People will add more fees to their transactions to entice miners to include theirs quicker.

That is how it is supposed to work when there is no more block reward. It will supposedly be marginally profitable as a whole.

The bitcoin wallet software allows people to add more transaction fees to their transaction to entice miners?

You won't be able to earn a living on transaction fees if your mining pool steals keeps them. Always ask your pool what happens to transaction fees. Eligius

There will likely always been another crypto-coin to mine when Bitcoin gets unprofitable, if your ASIC works with it, that's another story.

With the maximum of 7 Transactions per second and a transaction fee of 0.005 Bitcoin the maximium current return for mining a block without any minted Bitcoin reward is 21 Bitcoin

Two possible future scenarios will change this:

• 1. The Max Block size is changed requiring a fork
• 2. The standard fee of 0.005 Bitcoin is increased

The block reward halves ever ~1450 days.  So even the block reward wont drop to below 1 btc until 2032 and in the beginning of 2080 the block reward will be 0.00038147 and since bitcoins are infinite divisibility, there should always be a block reward.
That is not much but that could be worth a few dollars.  It might not be worth running the crazy dedicated rigs that some have now but it might be worth running a normal computer and hoping to get a few extra dollars each year.  This all really depends on the exchange rate at any given time.  If the price dropped to $10 btc tomorrow and stayed there for a while, you's likely see people shutting down their rigs (those that pay for electric, at least).

The truth of the matter is that the system is more secure the more people are mining.  Right now there are properly far too few people in control of mining and deciding how things work.  Think about what would happen if 3 or 4 mining pools got together and demanded a minimum transaction fee to put a transaction in a block.  Some miners would leave the pools, but if the operators shared the fees with miners, not many would leave.