1... to answer your first question it is demonstrably not true that denser materials are more durable. Gold for example is a very dense metal yet it is soft andf easily subject to wear and tear if carried as coins for example in then pocket.
2... If you skin and bones etc were of the same size and volume while being more dense then logic dictates that they would be heavier.
3... If a living organ is denser than another counterpart it does not necessarily mean that it is tougher and more durable, and in fact since such examples have never been found, it is impossible to say with certainty.
4... Well we can compare the density of gold with that of iron, for example. It is patently obvious that iron is more durable than gold in most applications, even though it is less dense than the gold. Hence it would not necessarily follow that a super-duper dense metal is more durable.
However in the case of gold, it does not easily react with other chemicals and hence does not therefore acquire a coating of oxide, etc.. whil;e iron on the other hand does have a tendency to rust (oxidise) in the presence of air with moisture.
Another dense but soft metal is lead and lead will oxidise and will also form a coating with sulfur in the atmosphere. So when discussing "durability" it is necessary to state the parameters of the conditions and environment.