The only reason not to mix and match brands is if they're paying you not to (really big discount). Builders buy whole suites because they usually do get a good sized extra bump, especially if they're fitting out a whole development, and also because it's just easier and they don't have to live with the consequences. Oh, one more reason for getting one brand is badges. If your appliances have prominent badges and you have some kind of obsession with things looking exactly the same, having the same badges and exact handles will be soothing. Without an emotional tic like that, or a bribe, er, discount, it's best to choose the items that best fit your function requirements, lifestyle, space, and budget, whatever they are.

As to your second question, would it be okay to get Therm/SZ coolers and Bertazzoni range, sure, get what you want. In general, however, I advise people to spend on cooking appliances first, because that's where the greatest difference is in how you'll use and enjoy your new kitchen. After that cooling, and washing a distant third unless you have really strong dishwasher issues.

SubZero is high end. Thermador columns are half a step down but a very good quality product. Aspirational. Bertazzoni is solidly mid-range. Do check reviews. Some people are fine with it, some aren't. If you're satisfied, however, and you like it, go ahead.