With btrfs there is really no need to. By default, calamares — i.e. the Manjaro installer — will create four dedicated subvolumes, being…
@ : your root subvolume, /
@home : the subvolume holding /home
@cache : the subvolume holding /var/cache
@log : the subvolume holding /var/log
btrfs subvolumes are like separate partitions, in that they each have their own inode tree, and they can (to a certain extent) be mounted with their own distinct mount options. However, they do all share the total amount of free space on the btrfs filesystem, and therefore, the individual subvolumes do not have fixed size limits, as would be the case with individual physical partitions.
timeshift also by default only creates snapshots of the @ subvolume, so that the system can be rolled back to a previous state without losing anything you’ve recently changed in your home directory, and without overwriting the system logs, so that you can still inspect them for the sake of forensics. And of course, the content of /var/cache is by definition disposable — a cache can always be rebuilt — and therefore its inclusion in a snapshot is not needed either.
That all said, perhaps you can take a look at this thread below in order to familiarize yourself with btrfs. 
Yes, there is, even though there’s no point. But you could shrink your system partition and then create an additional partition behind it. You can do this with gparted, which is a flexible GUI partition manager.
However, once you’ve then created the new partition and designated it to be mounted at /home, you’ll need to move everything over from the @home subvolume on the system partition to the new partition, and you’ll need to do that from within a live session — chrooting is not necessary — because once the new partition is mounted to /home, whatever was in /home before will not be accessible anymore.
I’ve created a tutorial a while ago that touches upon this subject, albeit that it was written before Manjaro started installing btrfs as the default filesystem. 
Still, the principle is roughly the same — you only need to make sure that you mount the @home subvolume at a temporary directory in the live session, and the partition you intend to use as /home at another temporary directory in the live system, and then move everything over.
After that, you must remove the @home subvolume on the main filesystem and replace it with a common directory called /home.
In closing, I would however recommend against it. I used to have a setup with distinct partitions as well, even though they were all formatted as btrfs — except for /boot, which was ext4 — but I’ve overhauled my entire system — without reinstalling, even though I did need to restore from a backup — to a unified btrfs filesystem with subvolumes. The only exception is my /boot partition, which is also btrfs, but it sits in front of the root filesystem, and therefore it was too dangerous to delete it and move the root filesystem to the left.
Really, you should stick with the setup you have. It’s very robust, and actually far more fault-tolerant than ext4.