Hello and welcome to HCM.
Thank you for your query.
A sudden increase in heart rate
just before sexual intercourse is normally seen in patients who are either diagnosed with a medical condition or have administered the drug 'viagra' for an enhanced sexual experience. If your partner used viagra and felt these symptoms, it is advised not to use the drug again without a doctors supervision. If none of these condition exist, he might require to undergo a cardiac examination to rule out any underlying undiagnosed cardiac conditions.
Burning sensation in the vagina during sexual intercourse could indicate the lack (or insufficient) amount of lubrication, that results in an increased amount of friction, that could irritate the vagina. You could speak to your doctor to help prescribe safe lubrication that could prevent this sensation in the future.
I hope I have succeeded in answering your questions, you could write back to me anytime for further clarifications.