Questions about prototyping a DMX Splitter
In the left bottom PCB there is a QuickBlow fuse, but in the original
  link it is a SlowBlow. I don't have these; will this be a problem?


That depends on the inrush current of the AC/DC adapters and the nature of any line faults your device might experience.  Generally, as long as the inrush current isn't sufficient to pop the fuse every time you turn the device on, using a faster fuse than necessary will just mean you blow fuses more often/unnecessarily.


  Would the HiLink HLK-PM01's have enough distance between each other?


This is a little dicey.  You have mains voltage on perf board, which is going to be a challenge, and generally I just plain wouldn't recommend it.  At the very least, you should remove as much of the unused copper around the AC connections as you can.  Better would be to either use separate enclosed AC-DC converters for each port rather than PC mount, or use a single AC-DC converter and then use isolated DC-DC modules to power each port.  Best of all would be to use an external DC wall wart and then a set of isolated DC-DC modules and avoid messing around with mains voltage entirely!  That will be the smallest and probably cheapest solution, too.


  I'm putting everything in one enclosure. I know officially a double
  enclosure should be used, however, there is really no space for it.
  And I intend to put the AC220/240V signals UNDER the bottom PCB which
  will be screwed tightly, so there is no possible way to touch
  220/240V. Is this 'acceptable'? I'm intending to use the device on
  stages with my music bands. The device will be under my keyboards
  stand, reasonably safe.


If the case is non-metallic, then this is generally fine as long as everything is mechanically secure.  If the case is metallic then it should be grounded via the ground pin on the power cord.


  The TVS types are 1.5KE18CA DO-201AD 1.5KE18 Bidirectional TVS diodes.
  Are these ok? I checked them, but I couldn't check the real usage.


Those are 18V bidirectional TVS diodes, with a clamping voltage of 32V, so by the time they activate to clamp a fault it may be too late for your transceiver.  RS485 requires that devices tolerate data line voltages of +12/-7V, so you should set your protection much closer than that.  Also, TVS diodes will be much more beneficial with something to limit the current into/out of the device when they activate, generally a 50-100mA polyfuse on the data lines is used.  Otherwise, a severe fault will just blow up the diodes before it blows up the transceiver.