What's the different between the private key and the signature?
A private key is a large random number which only one party should own. By combining the private key with the hash of the data and doing some other functions on that, a signature is created. A signature can then be verified by performing some other operations on the given message and signature to return with a public key which corresponds to the private key.
What does the digital signature consist of? Where did it come from?
A signature consists of two large integers which are determined by the hash of the message and the private key. It comes from the software that generated it. Here is some info on signatures:
https://en.wikipedia.org/wiki/Digital_signatureDanny says the "private key allows you to provide a digital signature that meets the requirements of specific transaction outputs in order to be allowed to use them as transaction inputs."
Provide a digital signature... to the blockchain, right?
The blockchain is not an entity. What happens is that the owner of the private key signs the unsigned transaction and the signature is then embedded into the transaction when it is sent.
Transactions technically consist of input orders, and output orders?
Kind of, they aren't really orders. Transactions consist of an input which corresponds to an outpoint, the output of another transaction before it. It then creates outputs that can be spent.
Why did you say "specific" in "specific transaction outputs"? Do some transaction outputs not require digital signatures?
Outputs are technically scripts. A script is essentially a program. In order to properly spend an output, the script of the input combined with the script of the corresponding output has to validate. After completing all of the commands in the script, the output of the program must be true (not 0) in order to validate. While there is a "normal" script used in outputs, an output can have all sorts of scripts, and the input that spends it must validate to true.
An example of a complete transaction is one successfully-executed output order plus the successfully-executed input order that the output order triggers?
See above.
Neither order will be executed unless a full set of requirements are met? Orders for transactions, such as an output and input order, are carried out only per certain requirements?
The scripts will be executed to validate a transaction. If it comes out false, the transaction is not valid. If it is true, the transaction is valid and is continued to be broadcast and can be included in blocks.
One requirement is typically valid order data (such as the currency, the amount...)?
Another is a valid private key?
Another is the digital signature associated with the private key?
Another is confirmation that the private key and digital signature match each other?
Output requirement is
Output requirements are
Output requirements include (a) a valid digital signature and?? the signature must be (b) validly coupled with its private key?
If output requirements are met, the requirements can then be used to try to clear a transaction input?
There are no specific requirements. See above.