Can vaping cause burning sensation in stomach and/or heartburn? and is it bad if you swallow the vape when you inhale it?

Yes: Yes recommend avoid gaping if having side effects

Yes and Yes: E- cigarettes may cause cough, irritation of throat/ mouth, nausea or headache. REF: https://www.bmj.com/content/360/bmj.j5543. Don't swallow vaping materials. As of 11 SEP 2019 The Centers for Disease Control and Prevention reported 6 deaths & > 450 possible cases of severe lung injury in 33 states & 1 jurisdiction related to vaping. The mechanism of injury is poorly understood at this time.