You do not have to put /home on a separate partition unless you wish to.
It is generally quite safe to install the entire Linux file structure to a single partition. On my primary computer, I do have /home as a separate partition; if something goes wrong forcing me to reinstall, the data in /home will be protected. Also, in case I wish to put a different distro on that machine, data in /home will be protected. But I didn't start doing that till I had been using Linux for six years and did not have any issues--if I reinstalled or upgraded, I just backed up essential data to a different machine.
In olden times, it was common to /var on a separate partition, in case log files grew out of control, but, with modern large HDDs, that's no longer an issue, except possibly in data centers, in the enterprise, and the like.
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Going back to your original question, you can't actually "split" a partition, but you can use Parted to resize a partition to a smaller size, then use the newly crated empty space to create a new partition. Back up any crucial data first, because, even though this usually works just fine, whenever you mess with partitions, there is a change that something would go wrong.