How do I maintain a steady address , or how can I enter a custom address (If at all possible)? Running Linux.
You can't make custom addresses. They are randomly-generated. You can create as many as you want, though.
What is a transaction's Time To Live is? Or in practical terms, when someone sends me Bitcoins, and my client is not running, how long do I have before the transaction is canceled (if it does, at all)?
There is no time limit. You'll get it whenever you come online. This could be years later. The sender doesn't need to remain online, either. The network handles it.
And a more theoretically driven question: I see confirmations rolling in for days after a transaction is complete.. In fact, in some transactions have confirmations already in their thousands.
In the long run, as BC grows, isn't this going to clog up the network?
They keep getting confirmed forever. I have transactions with 72,000+ confirmations. It doesn't "clog up the network", since people aren't actually confirming your transactions individually. They're confirming transactions that are unrelated to you, and this has the side-effect of making your transactions safer. It is expected that the network will be able to scale to thousands of transactions per second once it is large enough.