Is every program that ran on Intel Macs capable of being run on the new M1 Macs?
Is every program that ran on Intel Macs capable of being run on the new M1 Macs?

Generally speaking, yes, but it really depends.
Rosetta 2 is the compatibility layer that will allow legacy software to run on the new Apple Silicon.  It's this compatibility layer that will allow you to use your old software on this new chip much like how the original Rosetta allowed you to use software for PowerPC Macs to run on the new Intel based ones.
I very much hesitate to say that every program will work because there are always exceptions to the rule. Simple function apps or apps that don't make extensive use of hardware will probably work fine.  More complex apps or ones that make direct calls to hardware will likely have issues.  For instance, virtualization software like VirtualBox or Parallels won't work.   If you need Boot camp - that's off the table altogether.  So if you need to run these apps for whatever reason, you're out of luck for now.
Other specialized apps/products could have compatibility issues.  MusicTech recommends holding off for now until thorough testing can be done.  This is good advice across the board.  When your business and/or livelyhood depends on having a stable platform to get work done, switching to a brand new platform is risky, no matter how hyped and shiny the new product is.
If this is your sole computer and it's for work - hold off.  The software that you use is what brings in money and if nothing works, the brand new machine you just bought is effectively a paper weight.  It's like buying a brand new, state of the art robot to manufacture something only to forget to bring in all the new electrical and network connections to run it.
If you have multiple machines and you can continue functioning without it, then I encourage you to go get a new Mac and start testing (I can't wait to get mine in a week or so).  This way you'll know what works, what doesn't and what your options are down the road.