I'm a charity shop volunteer. I don't mind doing refunds for things people have bought and don't fit. We don't have a changing room - it had to be removed as there was so much ticket switching and stealing going on. So unless it's a jacket or something you can try over your clothes, you can't really trying things on. Most customers are very polite.
BUT, if you come in with an item you say you've bought from us but the tag has been removed and you don't have the receipt then no, you can't have a refund as you're a cheeky chancer. And no, you don't have the "right" to a refund or a replacement.
Similarly with people offering less than the asking price - it's a judgement call. Our shop is very busy and things get missed. We might not have noticed a hem coming down or a missing button and of course if that's pointed out I'll use my initiative and knock off a quid or two.
We also know easily how long something has been on the shelves because we use week codes. If an item has been out 2 weeks, not sold, priced at £10 and you offer £8, I'd probably let you have it. If on the other hand something has literally just gone on the shelves, no chance. People don't tend to make offers like that on clothing though, it's mainly the homewares or jewellery. Tea sets especially, we'll accept SENSIBLE offers on items if you ask politely.
Key words being sensible and politely...