All little ones do this, it's a phase they go through, and part of them learning a sense of self.
When she hits, because she will be fairly slow, you need to grab her hand befofe it makes contact, and hold it firmly. While doint that, put your face close to hers and say "No, that hurts!" in a loud voice, and make suree she breaks eye contact first. If she cries, don;t comfort her, she must learn that this is not acceptable. After a few days, maybe weeks, she will get the message, you need to be consistant and patient, and make sure that everyone else who has regular contact with her does the same, or she will simply transfer this action elsehwere.If she kicks, simply move out of range and ignore her completley.
Likewise tantrums and screaming fits - simply act like it's not happening. Be firm when strapping her in, and the ignore her completely. When she stops, kneel down and give her a kis and a cuddle and dry her eyes, and then carry on chatting to her as normal.
She will get the message that tantrums don not attract attnetion - which is their purpose - and she will stop them.
It takes patience and consistency, but she must learn that you are in charge.
This is the start of 'boundary pushing' that is a vital part of all child development, and as long as you put a firm policy in place ahd stick to it, she will learn that you are the one who has her own way, and she will be happy with that.
It's so easy to give in, when she screams in a supermarket and people look at you, but be strong, and make her back down - it will give her security, and make a happier child as she grows up.
It's not easy - but child-rearing never is!
Good luck!