Really good advice from BOS and Shipo.. I agree that you will get better as time goes on, because you were a different kind of athlete than the one you are gradually becoming. Consider your second question answered.
As to what you can do going forward, I have some additional advice. Shipo's experience with endurance training highlights one of the most important aspects of endurance running, which is proactive hydration. Think of all that water and tea, and how it is distributed around the clock. Running 5 kilometers or less, most of what you drink just before, or along the way, does not hit your system until you are done running. It takes about 20 minutes for your body to absorb that drink of water or Gatorade, and much longer for that H2O to find its way into the tissues of your muscles. The drink along the way helps more to satisfy your thirst and help you recover later, than it does to cool you off on these short runs.
With apologies to the folks down in the birthplace of sports drinks, where you train, the commercials sometimes depict an effect of immediate hydration that is misleading. Being well hydrated so your tissues can sweat effectively, starts 24 hours or more before exercise. The better prepared you are the day before, the better your performance will be when it counts. The minerals and nutrition you need for that workout need to be in place before you start. My advice, based on this fact and your athletic history, is to refrain from any sugared drinks during these hot runs. The extra carbs will only jack up your metabolism and produce more waste heat. Stick to water during these relatively brief workouts, and make sure your diet the rest of the day is rich in vital minerals (electrolytes).
Back in the day, you participated in fast-twitch sports that depended on a rapid conversion of stored sugar (glycogen) into energy. The key to success in endurance sports, on the other hand, is the gradual shift to fat-burning. There are two keys to transitioning from short-term bursts of energy to the type of slow-burn performance you need, and there is a time and a place for both. Intervals are still a helpful part of training the body to burn fat around the clock, but especially now, when it is hot outside, the long-slow-distance (LSD) training puts that process to work in a sustainable way.
As the others pointed out, now is the time to match your speed to your conditions. Gradually, your body will learn to run cooler with greater efficiency, when that's all you ask it to do. Starting out at a pace much slower than you are capable of, you will give your body the chance to shift from burning sugar to mostly fat. This can take a half hour or so, which means you will not really get to the place you want to be until you are ready to go longer distances. Make those first few miles as slow as you can go, with the realization that the real training is yet to come. Gradually tack on those extra miles over the next few months, and your body will oblige by beginning the transition from short-distance runner to endurance athlete.
Your account of the early experiments with running is like my own. I never thought distance was for me when I was younger, and started late with the same early disappointments. After a year or so, I was introduced to the Galloway method of distance training, the walk-run method, which is based on going much slower than potential. I was still capable of running fast, but my horizons for increased mileage expanded. Eventually I would compete in marathons, even qualifying for Boston, but it took years to get comfortable. My body had to change, and I am confident yours will, too.