The docking station does not allow me to connect the two drives at the same time on my computer
Everything seems to indicate that it should – the ASM1156 chipset that it uses, and the design and features it has in common with many other ASM1xxx-based two-port stations, and even the "Please do not remove your hard drive or insert a new one while the other hard drive is being accessed" note in the manual (typical of devices using this chipset, all of which support both disks simultaneously).
That said it might not perform as well with two disks compared to one – e.g. you can't swap disks in one bay while the other disk is in use (as that causes a disconnect), and at least with similar stations that used earlier ASM chipsets, only one disk could be given commands at a time so diskA-to-diskB copies would be quite slow in general (in contrast to computer-to-disk copies which would be fast). I'm not sure if they solved that limitation in the ASM1156.
I have done a number of backups this way. However, the cloning takes more and more time as disk 1 gets filled.
This is also slightly surprising as the cloning station should be doing just a 1:1 copy – it is unaware of which areas are in-use – but I suspect it's the result of WD Red being a SMR ("shingled" magnetic recording) disk instead of the regular CMR, so it's the writing to your 'target' disk that becomes slower over time.
Also, I am not certain it is "healthy" for the drive to wipe it and rewrite it regurlarly.
HDDs in general don't care; their physical storage doesn't wear out nearly as quick as flash storage of SSDs. For example, traditional CMR disks do not have any kind of wear-leveling and are fine with overwriting data in-place.
Although your WD Red is a SMR disk, which is somewhere in between HDDs and SSDs – the physical storage is still like that of a HDD (i.e. there is no "wear out" like flash storage has), however, due to the way data is physically arranged on the platters in SMR mode, such a disk has internal state like SSDs do.
Specifically, an SMR HDD keeps track of which areas are 'written', it has to rearrange them in background, and if a lot of data is written it might gradually lose performance unless you use TRIM (sort of like with SSDs). Again, it won't really wear out the surface, but the performance is not predictable.
Should I keep cloning my drives this way, or is it better to wipe disk 2 and only copy the differences from now on?
In your current method, you're one distraction away from accidentally swapping the disks and cloning your "last week" backup right over your "today's files" disk. Most file-level backup solutions would be more failproof as well as being much faster.
For example, Total Commander's "Synchronize Directories" feature is not very automatic, but at least it would make it a little more obvious in the initial 'Compare' window that you might be about to delete files rather than copy new ones.
(There are ways to automate it – e.g. a script can be written to check whether the target disk contains a "This is the backup disk" marker file, and to run robocopy.exe if everything matches.)
Your current method also doesn't make it easy to keep multiple versions (not without having a box of weekly HDDs or something like that). Many file-level backup systems do more than just synchronization – they support keeping a history of backups, so that e.g. in case of certain types of data corruption, you could still restore last month's files after you've realized you just did a backup of the corrupted version.