Is it obligatory to buy and slaughter an animal when fulfilling a vow (nadhir), or is it permissible to buy a ready-slaughtered animal and distribute it?

You must fulfill the vowed sacrifice in the manner you specified in your vow. If you intended to slaughter it yourself, then you must do so. If you only intended to distribute the meat, then you may purchase a slaughtered sheep and distribute its meat, because the original intent is that of the vower.