I'm a man and know more about mens standards, but if you can't back squat at least 1x your bodyweight you are probably pretty weak. Similar for deadlift. And these are just bare minimums. Most humans are FAR more capable than this. Maybe just multiply these by 0.5 for a women just based on genetic strength differences.
You can start with the bar if you want, you will eventually learn through experience based on your body your form for squatting. And the internet as well as being able to record yourself are readily available for practically everyone. Given that you can definitely learn the basics of form without necessary needing a trainer.
A trainer spending a year "strengthening your core" is called theft.
Yeah, people do worse in real life. They pick up stuff of varying weights all the time at odd angles.
Also, I would say that your grip is going to be a bigger liability in those situations.