Is there a way to improve your chances of finding miraculous fossils?

After yOu beat the game, go through the three battle Royales on each island. Once done wi these , go to the BBB base for the championship tournament. There you will fight Stella, Terry and Kent, then finally, Joe Wildwood. By the time you have finished all these tournaments, you should have acquired a head mask, a body mask, a leg mask and an arm mask. Like their color counterparts, when you wear one, you will only find that type of fossil. I used the head mask earlier today and did a quick run through of all the various dig sites, including the pay to dig sites. Since you are only finding head, dark and jewel rocks, there's not so many that you have to go to the cleaning room to clean out your case after each site. In addition to the above, I now have 9wondrous and 4 miraculous rocks waiting to be used. I wasn't,t paying strict attention at first, but I think I got most of the miraculous rocks at the pay to dig sites.

Put on the red mask and go to icegrip plateau with a fully upgraded sonar and it will be one of the yellow dots

When is one able to use the Fossil Cannon. I have heard anywhere from level 2-level 4

Yes. When you get the red mask go Icegrip Plateau in the Ilum island you may get lucky and find a few.