SandKa

It is for family videos and travel, why on earth get a Canon 5D mk2 / mk3? 
Doesn't really seem compatible with your purposes. 
 
Get a Panasonic G9 (or heck, even a Fujfilm X-T30) and enjoy!

I've made some more research and discovered that Fujifilm's video AF may not be as good (with regard to reliability) as I was thinking. It seems like it still needs some refinement or requires too much playing with the af settings (as shown on one of Philip Bloom's videos). Sony a7 III or Canon R would be a better choice but there aren't any good deals on them right now (to be within my constrained budget). There is a good offer for a Fuji X-T4 - 1000 EUR body only but I'm considering to back out a little and maybe start with some cheaper Canon DSLRs with which I'd have to rely on MF only with my Carl Zeiss 50mm f1.4 and not be disappointed by the faulty AF of Fujifilm. Which one would you choose - Canon 5d mark II or III ML Raw (MF with 50mm Carl Zeiss f1.4) or 5d mark IV (DPAF with Canon 50mm f1.8) in cropped 4k? Maybe give Fujifilm a chance but buy a cheaper X-T30, or wait for reviews of the new Canons i.e. r10 and r7?

Just weigh DPAF versus 14 bit RAW. If you go 5d mark iv make sure to get the c-log upgrade. 8 bit c-log grades nicely and you can’t deny the usefulness of good AF. But 5d mark iii RAW has that mojo, that I think a little bit of it got lost in the 5d iv. 5d ii I would only recommend if you have very little equipment; for example if you don’t have a lighting setup or want more lens options. Difference between that and 5d III is minor, and the extra money saved could go toward lenses, lighting, or both. Just weigh what is important to you. Any of the 5d routes is good. 

Buy one of these choices. They seem to make equally sense to your variantes of wants. Or, if money allows, all of them.😂 Sorry, usually i am not up to cute remarks, but your last post, in context to your og post, made me laugh. Still laughing. This thread will go on forever.😊

I've made some more research and discovered that Fujifilm's video AF may not be as good (with regard to reliability) as I was thinking. It seems like it still needs some refinement or requires too much playing with the af settings (as shown on one of Philip Bloom's videos). Sony a7 III or Canon R would be a better choice but there aren't any good deals on them right now (to be within my constrained budget). There is a good offer for a Fuji X-T4 - 1000 EUR body only but I'm considering to back out a little and maybe start with some cheaper Canon DSLRs with which I'd have to rely on MF only with my Carl Zeiss 50mm f1.4 and not be disappointed by the faulty AF of Fujifilm. Which one would you choose - Canon 5d mark II or III ML Raw (MF with 50mm Carl Zeiss f1.4) or 5d mark IV (DPAF with Canon 50mm f1.8) in cropped 4k? Maybe give Fujifilm a chance but buy a cheaper X-T30, or wait for reviews of the new Canons i.e. r10 and r7?

Assuming you're still reading this thread, I'd suggest the following:
Ignore all the tiny pieces of technical detail that the tech-obsessed and argument-prone contributors have shared in this thread and return to first-principles. First principle - get your shots in focus.  
Nothing else matters if a shot is out of focus.  If you're shooting kids or anything else that isn't under control then either get phase-detect AF or learn to manually focus.  I shoot similar to you and manually focus - it's a skill and requires some practice but it's do-able.  Getting shots in focus with the best auto-focus cameras is also a skill that requires practice. Second principle - get a nice looking image - whatever that means for you.  
The nicer the camera the more likely it will require colour grading and most people can't colour grade to save their own lives, let alone create lovely images.  Once again, this is a skill that can be developed, but making lovely videos requires (literally) a dozen or more skills so you just might not have it in you to learn to colour grade as well as edit, mix sound, master, learning NLEs, media management, etc etc.
If you don't want to learn to colour grade then you're going to rely on the picture-profiles from the camera and that will potentially limit the dynamic range and other image attributes, sometimes quite significantly. Third principle - get the first two right and then buy the camera and then don't look back.  Go learn about the other dozen skills.  Highly skilled people can create feature film quality results with any of the cameras you're talking about so there's a snowflakes-chance-in-hell that the camera will be a limitation, it will be your level of skill.   Fourth principle - if you get to here let me say this again.  The camera doesn't matter.  The only people that will tell you otherwise are camera nerds (like here in this forum), camera manufacturers (who want your money, over and over again), and camera influencers (who want the views and royalties and commissions and manufacturer kickbacks etc). Seriously.  Buy the camera that will get your shots in focus and then move on.

I am afraid of that. Sometimes footage which can be found on youtube shows disturbing "artifacts" (flickering red dots in darker parts of the picture looking like a noise). Maybe problems mostly occur in the newest experimental builds? There have to be some tested "safe modes" in ML for sure... Anyway, thank you for your input.

Hey, Sorry for the late reply, just saw your post.
That is a C/Y mount Zeiss 50mm 1.4 with a C mount adapter.
If you push the little silver button/lever on the back of the lens down or back (towards the rear of the lens), you should be able to unmount the lens from the C mount adapter.
After it's loose from the adapter you can get other adapters to mount it onto your Samsung NX, Canon EOS, or pretty much any other camera you'd buy in the future.