seagate backup

Yes it will work for Time Machine or other storage uses.

Just keep in mind that those inexpensive off the shelf Seagate and WD portable hard drives tend to fail far more often than more robust desktop drives.

for examples of more robust external hard drives,

see > https://eshop.macsales.com/shop/owc-mercury-elite-pro

and the faster > https://eshop.macsales.com/shop/owc-mercury-elite-pro-mini/usb-c

Yes, it will.

You will be required to format and partition the drive to Mac standards.

For the newest Macs that will be APFS formatting.