Can an oil drop in a Millikan's Oil Drop Experiment only have a negative charge? Wikipedia and Britannica seem to say the drops in a Millikan oil drop experiment are always negative, but can't ionization processes can either knock off or add electrons to the drop?
 A: Yes, droplets in Oil Drop experiments can be either positively or negatively charged.
This question is similar to How were the oil drops in the millikan oil drop experiment negatively charged?.
The dominant process for charging the droplets is not direct ionization of the droplet, but ionization of air molecules. For example, knocking an electron off an $N_2$ molecule produces an $N_2^+$ ion, and the loose electron can be picked up by an $O_2$ molecule producing an $O_2^-$ ion.  These ions can then react with other molecules in the air producing a wide variety of positive and negative ions that can attach to the droplets. Because negative ions turn out to have somewhat greater mobility than positive ions, droplets were more likely to pick up a negative ion and become negative, but Millikan actually had some control over the charge. Negative/positive ions will drift towards the positive/negative plate, so droplets near the positive plate are more likely to pick up negative charges and vice versa.  In the diagram (original here) shown in the similar question, the droplets are being injected near the positive plate, so more negative droplets would be expected, and any positive droplets will (relatively) quickly fall out of view since both gravity and the electric force are downward for those droplets.  If the electric polarity were switched, however, positive droplets could be studied.
