My eyelashes are white. Is there any medicine to make them black again?

It would be best to continue with one product at a time. If you have further questions contact the clinic where you purchased the product. Best, 

Latisse is used to help your lashes grow rather than fall out. However, you will still experience natural shedding of your lashes as they will still be going through the natural hair growth phases.

You can remove the hair as you wish and though new hair growth may occur, these hairs should return to their original growth pattern once the effects of Latisse wear off. Make sure to only apply a tiny amount of Latisse on the upper lash line and nowhere else to prevent this from happening again.

Latisse can cause pigment changes to your iris. Latisse can also cause pigment changes to the skin where it is applied. A photo would help to assess the color changes. There is contact information in the Latisse box with the directions. I would direct any concerns to the manufacturer. 

Yes you should be able to purchase latisse from a physician.  In our clinic we have treated alopecia and loss of eyelashes, eyebrows with latisse.  Although not perfect, there was a visible improvement after a few weeks of latisse

Latisse only affects the area in which it is applied or comes in contact with. This would be the upper eyelash line. If you are applying it to your public area, then it could encourage growth but if you are not, then it won't.