While a malfunctioning fan could cause image blurring I don't think I have ever seen results that indicate that normal fan operation is harmful for DSO work. However, when doing planetary work I never use the camera cooler since millisecond-long exposures are unlikely to be improved with cooling (and you're stacking hundreds if not thousands of subs, so noise isn't as much of an issue).
I'm not sure what you mean by "when the cooler fan was operating" as in my experience the fan runs continuously while the cooling is enabled. Is your fan stopping and starting by itself? That would seem odd, but maybe that can happen at very high temperature set points (like close to the ambient air temperature), however, I doubt it (meaning if your fan is stopping and starting then I'd contact the seller or the manufacturer to see what they think). If it is cycling then you might also need to check your power supply.
As for focusing, a well-functioning auto focus procedure is probably best (with a motorized focusing unit), but many of us use a Bahtinov mask and focus manually. That said, while a Bahtinov mask is easy to use and pretty reliable I'm not convinced that it will always result in the best focus or even a precisely repeatable point of focus. It's fairly easy and quick to use and it works pretty well but I wouldn't call it completely foolproof (since a user can misjudge the setting). There are, however, a few software-based focusing aids that use a Bahtinov mask and I'd expect that those would be a little more repeatable.
Bottom line, if you don't have an auto focus capability then I'd get a Bahtinov focus mask and see how that works out for you.