Normally, the way this is done is something like this:
1) RAID array with 1 or more redundant drives (so RAID 5 or 6) - allowing one or two drives to fail at once without data loss. Sometimes, this is done with RAID 10 which is effectively two arrays, you can lose more drives, but only if they're from different arrays. Given the rest of the scheme, 5 or 6 should be ok. It depends on the amount of data, costs, performance requirements, etc.
2) Offsite backup: Basically, take a full copy of the data and store it elsewhere.
Regarding theft, you need to allow for the data's security, so the offsite backup at least should use full disk encryption (if applicable).
Regarding your current setup (and the proposed one), do you need to allow for accidental deletes? You need to make sure removing a file won't automatically remove it from all your other copies. Same goes for file corruption.
If you use RAID 1 (i.e. mirroring), it should be possible to swap drives out and automatically sync the data, but personally, I wouldn't do this for the reasons above. What I'd do (and in fact do) is to use RAID 5 to aid in hardware failures, take a manual copy once a month which stays on site, and an encrypted copy once every 3 months which goes off site. If my data was super important, I'd likely go with RAID 10 rather than 5, but restore times aren't an issue for me.
Re: restore times. Having the entire array offsite on an encrypted drive is ok, but can you afford the downtime to restore it?
As for swapping drives, I use a case which holds the drives and has a slot in it which takes a SATA drive. Pop it in, do the backup, and hit the eject button. Done! SATA drives are handy like that as you can hot swap them.
Overall, I'd say your incremental backup approach, combined with RAID 5 and an offsite (maybe encrypted) would be good enough. But practice RAID skills on a virtual machine or similar, as if you need it, you may really need it.
With RAID 1, both drives MUST be the same size. So if you're upgrading the drives, then you can't just rip one out, put one in and expect it to rebuild. However, if the drive is the same size it should work fine. But seeing as you're wanting to expand the volume, it's not going to work. You're going to need to backup your data onto an external device, take out your hard drives (both of them), put your new drives in, create the new RAID array then put your stuff back on.
The TL;DR version: You can't mix hard drive sizes with RAID 1, which means you cannot expand the RAID volume.
Best Answer
First of all, if you're actually using RAID1 rather than SHR (Synology Hybrid RAID), the array will always be limited to the capacity of the smallest of them. It's because in RAID1 all data is copied across all drives that are part of the array. In a 3TB + 4TB + 4TB configuration the smallest disk couldn't fit the extra 1 TB of data.
SHR takes a different approach: it makes sure that each piece of data has exactly 1 disk of redundancy (or 2 disks in SHR-2). It would slice your 3+4+4 disks into a 3+3+3 part in RAID5 and a 1+1 part in RAID1, giving you 7 GB of total storage and no space wasted.
You can use the RAID Calculator to explore various configurations.
To check which RAID type you're using, open the Storage Manager, then Storage Pool tab in the left pane. If your storage pool is collapsed, expand it. Look at the RAID type.
Once you're ready to expand the volume (ie. all disks in RAID1 are now larger/at least 2 disks in SHR are now larger and the array has finished rebuilding), open Storage Manager again and switch to the Volume tab. Select your volume, click Action button on the toolbar and select Configure.
Finally find Modify allocated size label and click Max.