Yes, yes and yes. - But this just applies for an unsweetened mate.
A 2002 Danish study stated that an herbal preparation that included Yerba Mate, Guarana and Damiana ‘delayed gastric emptying, reduced the time to perceived gastric fullness and induced significant weight loss over 45 days in overweight patients’.
A Korean 2012 research done on mice determined that ‘Yerba Mate treatment affects food intake, resulting in higher energy expenditure, likely as a result of higher basal metabolism’. With a faster metabolism, the energy is spent faster, which can lead to losing weight. As other studies have explained, Mate’s effect on weight loss is probably due to the caffeine concentration, which also helps delay the absorption of fat.
Another study was done in Korea in 2015 with men and women with obesity. The results showed that after consuming yerba mate capsules for three weeks, the values of body fat mass and percent body fat decreased significantly, without producing significant adverse effects.
A 2012-2014 research done in Argentina showed that daily consumption of mate reduced the total cholesterol and LDL ("The bad") cholesterol by almost 12% in the course of 12 weeks. The research was done in two groups: one drinking approx. 50g of yerba mate (with 500 ml of water), and the other one, with double that amount. The results showed that in both cases the reduction of TC and LDL was considerable.