In response to your first question, it is grammatically correct both ways. You can choose the singular or the plural to avoid confusion, but that is not the case in this particular sentence. For the second one, informal American English is very forgiving with those inconsistencies of person and number. Having said this, if you would be writing a manual or formal script, you would want to maintain consistency in the person and say "Just take a Q-tip, stick it all the way down there (obviously you would use a more formal expression than this) and then apply it to your blemish." I hope this helps!

Depending on the context of the first sentence, it could be either "head" or "heads." If "their" is being used as a singular, gender-neutral pronoun, it would be head. For example: "I wonder who this criminal is and what is going through their head." <- Singular criminal of unknown gender, so "head" is used. "I wonder who these criminals are and what is going through their heads." <- Multiple criminals, so "heads" is used.