Your aerosols will have to have a lid (some security get really uptight about this, others don't care)
Hair straighteners definitely fine.
I've never taken tweezers - if I'm flying with carry-on only, it's usually a short enough trip that I can live without them.
Any liquid counts towards your limit, including makeup and moisturisers. But I've never had anyone check, although I don't think I've ever even come close to that limit. It would be a struggle to pack a 7kg backpack and have that much in there that's liquid.

Have a good trip!