The words in all four sentences could be seen as correct, depending on your meaning. I dislike using the sterile and biological term "females" to refer to women, but leaving that aside for the moment:
Sixty people, most of whom were females, liked the party.
This is a correct dependent clause where "whom" refers to people.
Sixty people, most of them were females, liked the party.
This is a little abrupt-sounding because "Most of them were females" is a complete sentence on its own. Inserting a complete sentence as a parenthetical in another sentence isn't impossible. In writing, it would be better to set it off with em dashes, though.
Your last two questions on that vs. which are more interesting. Which can be used to introduce an independent or a dependent clause. That can only be used to introduce a dependent clause. Most style guides would tell you not to use which to introduce a dependent clause. The commas matter, too. If it's an independent clause, it needs the commas, but the commas are technically incorrect in the one with that. Your examples are especially interesting, though, because they are a good example of exactly when it makes a difference when you use that or which. Here is how I would be most likely to read the following:
The animal, which is sick, needs treatments.
I would be most likely to take this to mean that a specific animal needs treatments because it is sick.
On the other hand, I would read the following differently:
The animal that is sick needs treatments.
I would take this to mean that the specific animal that happens to be sick needs treatments, but the animals that are well don't need treatments.