My Q is: I haven't formatted it yet a) because I don't know how:)
Applications -> Utilities -> Disk Utility
Suggest "exFAT" which will allow larger than 4GB individual files, and will work with Windows.
After you format it, before putting more than a sample file on the volume, take it to your Windows system and make sure you can be read/write. Once that is confirmed, you can proceed to dump stuff on to it.
and b) I want to know if I need partitions, and if yes, how do I decide what partitions to make and how big they should each be? The external hard drive is a Seagate one and Seagate don't actually spoon feed us through the how to's.
That would depend on whether you wanted to use it for more than just a transfer device. Otherwise don't bother.
NOTE: I DO NOT know what requirements Windows has on the type of partition table to be used.
Master Book Record (MBR) is typical for a Windows system, but I do not know if it will accept a GUID (which is typical for a Mac, but the Mac can read MBR)). But if you wanted a bootable Mac OS X partition, then you would need to use GUID.
This is one of the reasons you should test to make sure, after formatting, that the drive can be read and written by both Mac OS X and Windows. Setting partition type is in Disk Utility -> Partition -> Options, and changing the partition tables wipes the disk, so you want to find out before you spend a lot of time transferring lots of data to the drive.