Maybe, but they may just negotiate a high wage rather than a cut of the transfer fee.Yes. Even players as free agents can demand a transfer fee.
In terms of how much he is worth, there's a bunch of factors. First of all it depends on who he is willing to sign for, at which point it would be the highest bidder. If he only wants to Barca then his value is whatever Barca offer.
Second of all it depends on his contract. He only has one year left at which point he becomes a free agent. This will likely mean that Santos do not get a transfer fee. They may be entitled to some compensation, but that would likely be based on something like his annual salary so it probably would be relatively low. The third party ownership may also expire at the same time as his contract ends, depends on the contract.
It's a lot of unknowns, it may be that next season he would be free. In that case a typical valuation for him is likely around 20-30M. That's what the likes of Eto'o and Van Persie were valued at with one year on their contract. If Santos or DIS get some compensation next year his value would go up relative to that.
DIS are probably desperate to sell him this year since they likely don't get any benefit from him staying. Santos on the other hand can benefit from him playing and things like higher attendances because of him. Simply put, if Santos think they can earn more money by keeping him than selling him, they'll keep him. That's the number Barca need to beat to get them to agree to sell.
Neymar would liekly benefit from as low a transfer fee as possible because it would mean he could get a higher wage.