A knee sleeve provides support but does not function in the same way as a knee brace. Knee braces are designed and used to protect a previous injury from further damage. Knee sleeves are designed to protect the knee from future injury or potential damage.
Weightlifting gloves improve your grip on weights and make workouts safer. Hands get sweaty during a workout. When they do, your hands can slip. This can be annoying if you are doing pull-ups and keep falling off the bar. It is also dangerous if you are holding heavy weights over your body.
This is always a bit alarming, but it's perfectly normal. When you first start working out, your body responds by raising your heart rate and causing you to breathe heavy. Exercise gets a lot easier as you go along, and it's because your body starts adapting to your workout.