Optimizing fee payment for speed or zero fees/privacy? (Clients vs. e-wallets) As far as I understand the more fees you pay, the faster the delivery. What I don't understand is fees are given to kilobytes of data, not amount of money.

Maybe here would come handy a little deeper basic understanding how bitcoin works behind the scenes, maybe I should read this book?

I don't know, but the bigger the money the bigger the block size? Or the newer the money the bigger the block size? Or a little bit of both? As the miner solve more and more complex calculation problems(?). And the older the bitcoin block, the cheaper the transfer, regardless how big the amount is?

Consider 2 cases:

1st, you want to optimize for lowest or zero fees: time is not an issue. In this case as I understand bitcoins are transferred in chunks to save on fees. Does it also increase you privacy as well? How much time it takes to transfer a quadrillion dollars (or a little less), and what is the absolute minimum fee for such a large transfer?

2nd, you need instant delivery. I'm not sure about the fee structure (does it depend on the client or wallet you use?) but is it a fixed or variable % or a fixed amount per transaction? In the Qt client you can set an amount for fees but how do you calculate to spend the absolute minimum fees for an instant delivery? That would be just optimal, right?

As e-wallets use a share address, transferring funds in between bitcoin addresses of the same e-wallet should be free, and instantaneous, right? Instawallet?

Do I have the choice if I want to optimize for speed or costs (and maybe privacy?) with the various e-wallet providers? Let's say I want to spend instantaneously from an e-Wallet BTC 1 but I want to know beforehand how much I should transfer to that wallet in advance (slow transfer, zero fees) to include the appropriate (fast) fees.
The amount of bitcoins transferred is not the scarce resource you are paying for, disk space is. The distributed ledger that keeps track of the balance of each address is replicated on all participating nodes. That means that each KB more in your transaction is replicated thousands of times.

For the speed: all transactions are treated equal (except if they are deemed invalid as they in the case of a double-spend) so they are distributed over the network with the same speed. The fee comes into play once many transactions are available to be included in a block, i.e., they are still unconfirmed. As blocks have a maximum size (currently 1MB) there is a limited number of transactions that will be confirmed by a block. Miners will try to optimize their revenue from transaction fees of transactions that are included in the block, filling up with transactions that do not include fees.

Adding a fee to your transaction will increase the probability of it being included in a block, i.e., being confirmed.

The transaction size is dependent mainly on the number of inputs that are claimed. As the number bitcoins from an output have no influence on its size the number of bitcoins transferred in a transaction does not influence the transaction size.

As for e-Wallet internal transactions: they are likely not handled by the Bitcoin network but internally, thus completely independent from the network rules.