Open Question: Can I bring this stuff on a Carry-On bag for a plane flight?

This week I am going on vacation internationally. My mom is making my brother and I take carry-on bags for our stuff instead of a checked bag (I assume it’s cheaper?). Then, the things we can’t take on our bags (shampoo, conditioner, big bottle of lotion, etc.) or fit in our bags will be taken in her checked bag. So I have a question. Can I take eyeliner, mascara, mini sized lotion, mini sized soap, and mini sized perfume (all from bath and body works except for mascara) on the plane ride with me in a zip lock bag? I don’t want to get anything thrown away that I might need.
Oh and since I am a girl, can I take a purse and a carry on? I have money and things that I want to take with me.

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