That was very close to 10k, but it seems that is no problem for you now so you are making good progress. I've started taking water on longer runs now. I do drink before I go out and straight afterwards with my breakfast. I aim to run at the cooler times of day.
I was not checking my heart rate today, but I stayed out of zone 4 at a gentle pace. If I try to stay in zone 2 then I tend to go just over that anyway. I expect my zones are different to yours.
RE: trying to stay out of zone 4 while doing cardio is easier said than done