The lethargy bothers me - a vet visit is in order pronto. You will also need to find out from your vet ~if~ she can be wormed right now - I am not familiar with the newest medications for this in relation to a nursing queen. In answer to your question about worms being transferred from cat to human, yes, some of them most certainly can be transferred.
But once your vet has examined her and she is again home with a clean bill of health, you should know that nursing queens do lose weight and resources while nursing. Being responsible for the total nutritional needs of five growing babies takes a lot out of a girl! It isn't uncommon. You will need to up her food intake dramatically and of course, you will need to have her eating a good quality canned and dry kitten food right now. Give her as much as she wants along with all the fresh water she wants to take. It doesn't hurt if you supplement her with some foods heavy in calcium such as cottage cheese or plain yogurt right now either. My girl won't eat people food (other than chicken or turkey) so I gave her a calcium tablet once a day - my vet instructed me on the proper amount and daily dosage based on her weight, so if you go this route, ask your vet to weigh her and tell you how much to give as well as when.
You might also want to consider trying to introduce the babies to a high-quality canned pate-style kitten food a little earlier than is normal (normal is between 4 and 6 weeks) in order to give your girl a bit of a break. See if they won't take food as early as 2 to 2 and a half weeks - in other words - NOW. They will walk through it, track it everywhere and do anything else besides eat it at first but if you confine them in a small space for a day or so (I use an extra large dog crate for this) with their new food bowls (I like the wide-mouthed saucer-type bowls with a heavier bottom so they can't push it around) and a small litter box (don't use clumping) they will get the general idea pretty quickly.
Please let us know what the vet says and how she is progressing.