Do I "need" to have all my iPhone apps copied to my iTunes on my Mac when i sync?

If you are so low on disk space you are essentially using your phone as a storage device for apps, I suggest you get a bigger disk on the Mac, because you will run into all sorts of issues shortly. Seriously.

Not really, I haven't synced any apps with my mac since 2012. It is nearly impossible to use just a standard mac with any iOS device. The new macs come start off at only 128GB, of which most is used by the OS and important applications, then fill that up with device backups, and then the 16 or so GB of apps which would be on there and good luck. Right now I have a 32GB iPad and a 256GB Retina MBP and I wouldn't even try it, just keep your important things on your computer and don't worry about re-downloadable apps.

Can you not keep copies of apps on your Mac? Yes. Should you do this? No.

Get an external drive if space is tight. But, if you delete an app and Apple removes it from iTunes, you're out of luck. External drives are cheap and I think it's worth the peace of mind to know your apps will always be available, even if deleted from the phone.

Do a Time Machine backup to an external drive (which is a good thing to do for everything on your Mac), then delete the apps from your Mac.

If you sync your iPhone with your Mac, say yes to the message about copying apps across to your Mac, otherwise they will be removed fro your iPhone. This will create add those apps only to your Mac. You could have not deleted those particular apps in the instructions in the last paragraph, but it is easier to remove all, then let the sync add the right ones back.