"Normal" doesn't really exist. It's clearly not normal for you. She may find some of your behaviours aren't "normal". Lots of people love thrift store shopping, and think it's great from both a bargain and environmental perspective.
Unclear where the "knickers" idea is coming from - I don't recall seeing any charity shops selling used underpants. Maybe brand new unopened packets - in which case there's no issue.
I've got a few relatives who enjoy charity shop perusals, and buying stuff on vinted etc. It gives them joy to find a bargain - and that's understandable. Also understandable why they may not wish to spend a ton of money on brand new kids clothes - they grow out of them very quickly.
I do understand why you would be upset if the clothes are obviously dirty/smelly/not fit for use. That said, even brand new clothes can have a bit of a nasty smell. In her situation I would usually wash any charity shop finds before I gave them to anyone else, especially a child. I would also not expect the recipient to necessarily want them - and it wouldn't bother me if they didn't because fashion and clothing is a very personal thing.
As for re-gifting things that you've given to her in the first place: that's a different thing entirely. That is understandably something you'd be a bit annoyed about - though given she's elderly she may have forgotten it was you who gave it to her. She may associate you with the items but gotten the association incorrect. That sort of forgetfulness is pretty normal for older people (you asked what's normal and what isn't).
As with all things the way to deal with this if it's bothering you is to communicate with her about it, and to do so in as kind a way as possible. It's lovely that she wants to gift things to you and your family - maybe instead of being negative about it you could approach this by giving her some ideas of the sorts of things you would actually like for your children: so, you would like some GAP kids shorts in whatever size they like. Or you'd like a Polo Ralph Lauren t-shirt or somesuch. That'll give her things to look for (which thrifters often enjoy). And if you don't want clothes then ask for something else - some people collect mid century Pyrex for example (not my cup of tea, but hey - each to their own).
As for her selling stuff on FB marketplace - unclear what your issue is with that (your account of what is happening there seems a bit unclear: you say: "as any toys she would buy for DD on FB marketplace for free, she would then keep at hers but would then proceed to sell them next week on FB marketplace for ££!! And not tell me..." First, if she's getting them for free on FB marketplace then she's not buying them - she's being given then; Second, you say she's keeping them and then selling them...what's wrong with that?? She was the one who got them, why does she have to tell you what she is doing with stuff she's getting for free on FB? Do you mean to say that she's found things on FB Marketplace before, told you that she got them for your child, but never actually gave them to your child and instead sold them? Well, given your attitude to her finds and thrifting she may well have gotten the impression you weren't all that fussed about whatever the item was, so she decided to sell it. Or, put another way, you can't have it both ways. Plus, how do you know she's sold the stuff? Seems a bit odd to be keeping tabs on what people are buying and selling.
Also unclear what you mean about her being "stingy" - what are you expecting from her? She's getting your child gifts, what more do you want?
If you don't want to communicate with her about this then the way forward would just be to say thank you when she gives you stuff, and then then just donate whatever you don't like back to the charity shops. But put it in a donation box that won't be locally distributed.