I can see where the OP's coming from, and anyone else who didn't have good role models to be fair. I came from an immaculate home even though my mother didn't clean personally so I came away knowing that homes should be clean and tidy and that sheets should be changed every week and socks and pants and shirts changed daily. My family was interested in food and a bit continental so I was used to different things and different views and brought up between country and London by people who were practical and down to earth even though they were a bit posh.
DH on the other hand had a mother who hadn't been set a good example and who wasn't interested in learning about practical things. I think she sort of thinks that very clever people shouldn't sully themselves with cooking and cleanliness and it's a very peculiar type of snobbery.
But OP you can do all the things you mention. You just have to read up about them and practice them and be confident and accept you might do it wrong a few times as part of the learning curve.
I was taught to cook by a famous lady but learnt more after the course by reading, actually reading Delia's three part Cookery Course, I read the leaflets about nits and after DS had to have a number 2 cut after I cleared up the vilest infestation known to childkind. Make it an adventure about creepy crawlies, count them and use tons and tons of conditioner in the bubbliest baths with more plastic toys than you can imagine. After that, when dd was about 8 months and had no hair I nit combed her after every bath - to get her into good habits and you know it prevents them too. You might comb out the odd fat gestator but if you do it two/three times a week they aren't around long enough to lay too many eggs.
First Aid and health care - read the baby book, feel if they have a temperature and if they do and it doesn't go and won't settle get their ears checked.
Brush their teeth, take them to the dentist and optician, immunise them, keep calm around them, praise them and love them. You'll be fine.
Dororthy Nolte summed it up for me
“If a child lives with criticism, he learns to condemn . . .
If a child lives with hostility, he learns to fight . . .
If a child lives with fear, he learns to be apprehensive . . .
If a child lives with pity, he learns to feel sorry for himself . . .
If a child lives with ridicule, he learns to be shy . . .
If a child lives with jealousy, he learns to feel envy . . .
If a child lives with shame, he learns to feel guilty ...
BUT
If a child lives with tolerance, he learns to be patient . . .
If a child lives with encouragement, he learns to be confident . . .
If a child lives with praise, he learns to be appreciative . . .
If a child lives with acceptance, he learns to love . .
If children live with approval, they learn to like themselves..
If a child lives with honesty, he learns what truth is . . .
If a child lives with fairness, he learns justice . . .
If children live with recognition, they learn to have a goal.
If children live with sharing, they learn to be generous.
If a child lives with security, he learns to have faith in himself and those about him . . .
If a child lives with friendliness, he learns the world is a nice place in which to live . . .”