When you pay by card or Paypal the seller pays any fees related to the transaction. Does BTC allow anything similar? It would make it more customer friendly.
No, but I've seen merchants giving their customers discount when paying in BTC. I guess that discount more or less corresponds to the fee they save compared to accepting credit card or other payment methods, many of which take quite a cut. So while Bitcoin doesn't work like that on a technical level, merchants could still take transaction fees into account when accepting payments.
Yes it would probably help adoption, no Bitcoin doesnt offer it. This is the reason credit cards can get away with 3.5% fees, because the consumer doesn't see it.
Also credit cards offer consumers all sorts of perks for them using credit cards instead of other means of payment. That those perks are mostly financed by credit card fees, thus the merchants, thus the consumer is happily ignored since there are enough steps of separation inbetween.