The seed allows you to generate the private keys? You can generate the private keys as many time as you want from the seed?
Yes. Using the seed, you can convert it into a string of letters and that would be your master private key. Using that, you can generate as many private keys as you want.
Private keys can be stored either on the usb device, or online like on bitgo, or locally on my computer using Electrum?
Some online wallets generates the wallet only from your seed, they don't store it. But yes, it can also be stored on any storage medium. Its like a key.
How do you generate the private keys from the seed for each of the 3 situations (device, online and locally).
The wallet does it for you.
Can I use the seed from Electrum on Bitgo so they generate my private keys again?
I'm not aware of what standard Bitgo adopts. For Electrum, they use their own exclusive standard which most(all?) wallets do not currently use. Hence, you can only be importing the seed into an Electrum wallet.
What's the point of saving the private keys on the usb device if you only need the seed?
There's honestly no point.
I could only save the seed on a few pieces of papers in 3 locations and then I could generate the private keys anytime and anywhere I want with those? So why saving the private keys?
Exactly. Exporting the private keys would likely just cause more confusion.