Lack of a fossil doesn't mean something was not there. A fossil can *prove* that something existed but after all we hear about how difficult it is for something to be fossilized that it's remarkable that there are any fossils at all, you can't prove that something didn't exist because of a lack of a fossil. What do you mean by *modern*? Something that is alive today? If that's the case, a google search on *living fossils* and *bat fossils* will provide some links to discuss this.
Yes. If evolution is bunk, then all creatures today existed in the same form hundreds of millions of years ago. Am I not correct? Since animals do not change, then we should see the single hooved horse fossils at the same time we see 5 toed versions. My point is you do not see that at all.
There are lots of other animal we do see fossils for but the farther you go back... all you see are animals that do not exist today. You would think that you would see fossils of modern day animals but you do not.
Shark fossils and crocodiles do go back pretty far... but not even close to far enough to say they never changed.