How are Uranium and such materials made
Some radioactive materials are made by man, others have been parts of earth's rocks since they were formed

Radioactive materials are not all the same. some are man-made and some have been with us since the creation of the planet (so are indeed the product of old exploded stars).

The best way to tell which is which is to look at the half-life of the atoms involved. Half-life is a measure of how fast an isotope decays. It is the length of time it takes for half of the amount of substance to have decayed to something else. So half-lives with the same sort of size as the age of the earth are quite likely to be primordial (which basically means they were present when the earth was first formed). Other compounds with shorter half-lives would have all disappeared by now even if they were present then. They are synthesised by man.

238U (by far the most common isotope of uranium) has a half-life of ~4.5 billion years (roughly the same age as the Earth) so quite a lot of the uranium present at our planet's birth is still around. 239Pu (the isotope of plutonium used in nukes) has a half-life of ~24 thousand years so even if there was some around when the earth was formed there wouldn't be any of that left. Plutonium is created in nuclear reactors which can be designed to generate enough to make an indecent supply for the military. Having said that, a very small amount may be generated naturally in uranium containing rocks as part of the normal decay pathways of uranium or as part of natural nuclear reactors (occasionally in geological history uranium rich rocks have created the conditions for significant nuclear reactions which produce more plutonium and other materials than simple decay of isolated uranium atoms).

Other, more common, elements sometimes have radioactive isotopes. A small proportion of potassium, for example is 40K which has a half-life of ~1.2bn years (so quite a lot of the earth's original stock is still around and is the largest contributor to radiation in living things which all contains a lot of potassium). 

There is little danger of running out of primordial radioactive elements as we are not using them fast enough. The man-made ones can be made in nuclear reactors if they are set up the right way (and we have way more plutonium than we know what to do with; but many rare isotopes used in medical research are made in specialty reactors where the risk is that a reactor shutdown might limit the supply).

If you want to know where all the elements originally came from, there is a good Wikipedia article with a periodic table that explains the detailed origins.