Is a private key used up when part of the bitcoins it controls are sent?

Here is my current understanding of Bitcoin:

I have 10 bitcoins in my wallet.

If I send 5 bitcoins to someone else, I am sending the private key from my wallet to somebody’s public key address.

Those are combined into a new transaction that is later confirmed by miners. The miners confirm that I owned the bitcoins by checking my private key, and that the receiver’s public key is valid.

Then, the miners create a new private key that is sent to the receiver’s wallet.

On a simple True/False basis, is everything I have said right so far?

If so, what happens to the remaining 5 bitcoins in my wallet? Do they magically get a new private key, or what? How does my wallet know how many I have left, and how do the remaining bitcoins get a new identity?

Who gets Bitcoin transaction fees?

Whenever I send bitcoins from one wallet or one exchange to the next there is always a fee. This makes sense with the exchange sites, they are just collecting the fee so they can make a living. What about the open source wallets that I’ve installed on my computer?
Surely, nobody is collecting my bitcoins because my transactions are too long! So, is the “fee” part of the Bitcoin algorithm? Do the coins that are confiscated in the fee go to Bitcoin miners?

Also, when does the fee start? I noticed, if I send like 0.05 bitcoins there is no fee, but if I send 0.1 bitcoins there is a fee.
What if I just sent 0.05 bit coins twice? Or is it if they are in the same block I will get a fee, so I’d have to send them twice (and 10 minutes apart)?

How does Ripple synchronizes its ledger?

Bitcoin decides on a global clock by the blockchain – every mined block is another tick of that clock.

In Ripple, there is a global ledger that keeps advancing in time – the ledger number keeps increasing all the time, and the ledger represents the state of the system at time t.

What synchronizes this ledger? How do different Ripple nodes know when they should advanced their ledger counter?

Why is my transaction not getting confirmed and what can I do about it?

I sent a transaction

  • without (or with an exceptionally small) transaction fee
  • using extremely small or unconfirmed inputs
  • while the stars were not standing right.

For whatever reason, I have been waiting forever for my transaction to confirm.

Why is it taking so long for my transaction to confirm? What can I do to speed-up the transaction’s confirmation?

This is a canonical question serving as a lightning rod for the flood of “unconfirmed transaction” questions we are experiencing lately. Please provide a detailed and broad answer to serve a wide range of these questions.