Does production date affect compability or lifetime of a drive?

Actually it's a good thing that you have mixed batches.

HDD manufacturers sometimes have faulty batches. Disks from a bad batch tend to fail around the same time. That's no good because your RAID redundancy works on the assumption that disks die randomly.

Some people intentionally buy different disk models or try to mix disks from different batches to avoid this issue. And you've received mixed batches without asking for them.

I wouldn't worry too much about these two. You can run a little stress test to make sure they're good, for example fill them up with zeros.

If the drives were stored at a cold, dry place not exposed to sunlight or other radiation, their age should not make you worry.

However, some manufacturers update hard- and firmware between different batches and without notice. This can lead to unexpected behavior. E.g. Western Digital recently implemented SMR, which makes the new batches less suitable for certain use cases.

That is the reason why I prefer disks from the same batch, but as the other answer suggests, there are also reasons to mix different batches.

However, at least you want to make sure all disks run the newest firmware.