Is there any possible way to get very faint positive home pregnancy tests and not be pregnant other than chemical pregnancy?

Depends on details: Home pregnancy tests are very accurate and not affected by foods, herbs, common illnesses, sexually transmitted diseases, or medications. A correctly read urine test gives a reliable result 3 weeks after sex (3 weeks after when conception might have happened) or 1 week after missing a period. A faint positive result can be real, so possibly there was a transient pregnancy for a few days.

Not at your age: A peri-menopausal woman my get a faint positive without being pregnant. Chemical pregnancy is a pregnancy that spontenoulsy terminates at a very early gestational age, but is still a pregnancy. Retest in 4-5 days, unless you get a period by then. Use first morning urine and follow instructions for the test carefully. If you do not wish to be pregnant, use contraception all the time, every time.