That is not too low if the diet is properly designed. There are many clinical studies run at much lower numbers, the so-called very low calorie diets (VLCD) which are generally set at 800 calories per day.
Too low is a function of protein and micronutrient requirements. If the body is getting sufficient protein, essential fats, trace minerals, and vitamins then that calorie range is sufficient since adipose tissue (fat) can contribute 31.4 calories of energy per pound of fat mass per day. If the OP has 100 lbs of fat mass, he can get 3,140 calories worth of energy from fat, which if supplemented by 1200-1500 calories from diet, puts him well over 4,000 calories of available energy. His near term dietary needs are driven entirely by the nutrients he needs that cannot get from stored fat, such as protein.
As for "starvation mode" that is entirely bro science. On a low calorie regimen your metabolic rate will drop, but not to zero. The rate of metabolic decline has been measured clinically at 23% for a cohort of obese women on an 800 calorie VLCD. In the famous (infamous?) Minnesota Starvation Experiment, the reduction was estimated at 45% as the men approached essential fat levels (think skin and bones / concentration camp survivor appearance). On a 1200-1500 calorie diet the rate would be something less than 20%. If, for example, the starting BMR was 2,000 then after a reduction of, say 15%, the new BMR would be 1,700 and the benefit of dieting would be the difference between calories in and 1,700, not calories in and 2,000.
However, you do need to keep the body in anabolic mode to punish the fat and promote muscle maintenance. That will force the body to get its calories from the stored fat mass and not by catabolizing muscle. Exercise that creates and maintains high skeltal muscle tension, such as lifting weights and HIIT, upregulates growth hormone production and keeps the body in anabolic mode. Tension is created by lifting HEAVY.
That is why you lift weights when trying to lose fat. Lifting is the same as any other cardio exercise when it comes to burning the fat itself (energy expenditure is energy expenditure), but the hormonal effects created by lifting cause the body to prefer destruction of fat over catabolization of muscle. HIIT causes similar hormonal effects and improves fat burning over aerobic cardio for a number of biochemical reasons; study up on anerobic / Cori cycle metabolic pathways versus aerobic / Krebs cycle pathways if you want to understand the details.