I don't have much experience with English boots other than my rubber pair I got because they hug my leg and look decent, but are weatherproof for mucking. However, having said that, yes, zip is better than lace for just around-the-barn stuff because they're much easier and faster to get on and off.
As to your next set of questions, putting your weight in your heels is still something you have to think about to get used to doing, even with boots on, unfortunately. I think your mind just ignores extra weight on your feet unless it's really significant, so I don't think it will help as a reminder. The reason for boots with a heel is so that a.) the smooth casing of the boot over your ankle and up your leg doesn't get a shoe tongue caught up in the top of the stirrup, and b.) the heel keeps the foot from slipping through the stirrup and extending to get caught by your ankle. The heel of the boot will be outside the stirrup so it doesn't interfere with your ability to put your heel down. Hope this helps :)