1. Did you apply the cosmetics on your face?

2. Did you wear the cosmetics on your face?

3. Did you put the cosmetics on your face?

(Are all correct and the same? Can we use 'lotion' instead of 'cosmetics?)

All of them are correct, but 1 and 3 are most commonly used.

"Cosmetics" includes more than just lotion, so if you decide to use "lotion," remember that there are other things that can be applied, such as mascara, lipstick, rouge, etc.

Yes, all three sentences have the same meaning. They all inquire whether you applied cosmetics to your face.

Regarding your second question, "lotion" refers to a specific type of cosmetic product that is typically used for moisturizing the skin. While the terms "cosmetics" and "lotion" can be used interchangeably to discuss products applied to the face, it's important to note that cosmetics encompass a broader range of products, including makeup, skincare, and other beauty products beyond just lotions. Therefore, if you specifically want to refer to a lotion, it's more accurate to use the term "lotion" instead of "cosmetics."