If my understanding is correct, I have to wait for coinbase to sift through their money orders and make the transfer themselves which is then instantly received once they get around to it. After which, I wait 10 to 30 minutes for it to go through on the bitcoin network.
Yep. Bitcoin transactions are instant, but when you have your coins in Coinbase,
they are holding and spending them for you. It's like a bank in that you put in money based on the promise that you can get it out again when you want.
The vast majority of Bitcoin wallets give you control over your private keys, but a few online wallets don't (and no exchanges do, as far as I know). You should check
Bitcoin.org's guide to different types of wallets, if you ever need a more convenient way to send than your paper wallet.
Oh my gosh! So much for speedy transactions. I'm hoping that this segwit thing will help speed it up, but who knows if it is enough.
SegWit's aim is to increase the capacity of the network so that you get quicker
confirmations. Sending itself is still instant.