I haven't exactly read the details, but from the gist of it, it seems you have lost a considerable amount of weight. Congrats, to some extent.
To answer your topic question literally, No, to have lost a lot of weight isn't really correlated with being healthy. I think what you mean to ask is if you have lost enough weight to be labeled "average body weight", which says little about if you are taking care of your body on its own.
BMI, I personally discredit it, I think it is outdated and too simplistic, but it still provides a general guideline I suppose. As you somewhat seem to know, BMI doesn't take into consideration several things, gender, age (older people often have lower bone density, thus they are lighter for instance), BF%/ muscle mass %, etc. I'm 5'10 and I weigh 175 now, and I'm quite proud in saying the BMI states I JUST passed the mark from average, to overweight. Why am I happy about being "overweight"? Because for males in particular who spends quite some time in the gym, it means that they have a good bit of muscle in them that the BMI overlooks.
So, if you really have been eating healthy and doing cardio/weight training and have become 152 pounds, kudos =P. You can assume you have gained a bit of muscle from the weight training, so you can be towards the upper extremities of "average".