I have a few problems, and I am not sure how to solve them. I transferred ethereum from Coinbase to a wallet that I originally created on a Mac. The initial sync was not yet complete, and it is taking days and days (and slowing down my other work). I haven't yet "received" the ether into the Mac wallet. Can I sync the blockchain on another device and receive the ether there? I am a novice here. Thanks for any feedback.
Yes you can most definitely have the same Ethereum account on more than one device, all you have to do is import the private key.
Which wallet are you using? I'll assume it's mist, although I believe this method will work for a few different wallets. On your mac navigate to the folder
~/Library/Ethereum/keystore (You might have to copy and paste this path in Finder
Folder --» Go to Folder in the top bar menu) now copy the file you find in there, this is called your keystore file and it contains the private key to your account.
Now on your other device (if you're using mist) click on
Accounts --» Import wallet file and drag and drop the file you copied from your mac here. You will then be able to access your account on the new device.