Can I donate blood like I used to? HPV 16 positive. Will it be detected in the blood test? Will I cause harm to others if I donate? Shall I stop it!?

Of course. I'm concerned about you for asking, and whether there isn't some misunderstanding. You say you are 29, and have had breast cancer -- this should have been a consideration as to whether you can donate blood, rather than your HPV-16. The HPV virus will probably never be a problem and if it is, it's manageable if you comply as I understand you have done.
Continue donating. Do answer all the health questions honestly, prior to donating. HPV infection per se is not a contraindication to donating blood, and will not cause harm to recipients of your blood. It is kind of you to be a good citizen and providing service to fellow humans.