Is it safe/possible to mix the chemistry brands together, such as using a Kodak E6 first developer, with trebla starter, or using something like kodak developers with trebla/whoever elses fix/other steps, and likewise with C41? Or is it more usual to just stick to one brand troughout the entire process?
You should really stick to one brand, and line of chemistry. That goes particularly for developers and starters, although switching to a different bleach/fis is less of an issue.
Since Kodak has changed to Bleach III, and since Kodak and Fuji have changed to new methods of stabilzation for some processes, crossing chemistry can become a real pain. You can mix one fix with another bleach, or one developer with another bleach, but DON"T mix two bleaches together, or one bleach and another starter. Starters are paired with the working solution and can be a mess if crossed.
I would not do it with color developer starters and replenishers from different companies, though you would probably be OK using one company's developer, another company's bleach, then another company's fixer, etc.