Do teleconverters slow down focus? This was very true on DSLRs, but not really a factor with mirrorless. The difference has to do with both how much light gets to the phase detect cells (DSLRs only let a portion of it through their partially silvered mirrors), but also a bit due to how the masking above the phase detect cells works (she blinded me with Geometry!). On a DSLR, f/8 was really the maximum any focus performance could be attained, and even that was noticeably slower than f/5.6. On a mirrorless camera, I've used f/11 without seeing any real degradation of focus. There's another thing to consider, too: on a DSLR, using smaller aperture lenses reduced the number of phase detect cells that were active (again, geometry). On a mirrorless camera that doesn't happen: all focus areas are still active.
Is it better to use a teleconverter or crop? Generally, all else kept equal, teleconverter, particularly the 1.4x versus a DX crop (1.5x). Cropping effectively reduces visible dynamic range (DR). A DX crop reduces DR about a stop. If you keep ISO the same as the crop when using the teleconverter, you're better off. If you increase ISO by a stop because of the change in effective aperture with the teleconverter, you're about equal. The other attribute that's impacted is "resolution". I put that word in quotes because generally you're going to examine this at different magnifications (e.g., you're going to print the DX crop image the same size as the teleconverter image, which requires more magnification). In a DX crop you're still getting the same overall resolution on the subject, but you're going to be blowing it up bigger in the final image. With the teleconverter, yes, you're losing a bit of the lens' resolution, but you're not magnifying that decrease. In most cases, the teleconverter will win at the same output size (again, all else equal).
Are the built-in teleconverters (400mm f/2.8 TC VR S and 600mm f/4 TC VR S) better than the external teleconverters? A hesitant yes. The teleconverter in the TC lenses is tested and aligned with the lens in the factory. It has to meet certain high standards in QA to leave the factory. External teleconverters are tested separately from the lens they may be mounted on. Sample variation starts to come into play. I've seen an external teleconverter and lens perform better than my expectations, I've seen them perform worse than my expectations, and in trying to assess why that was, it almost always comes down to sample variation. If the lens and teleconverter are at the opposite ends of their factory tolerances, you get worse results. That said, most people wouldn't notice the small differences. Because I'm running Imatest and sometimes FoCal results on every lens/teleconverter combination, I usually see them first in the numbers, which gives me something to look closely for in the actual images.