(1) Not only is it possible but it has been documented on pretty much every generation of x86 processor. Go back to the 8088 and work your way forward, every generation. Clock for clock the newer processor was slower for the current mainstream applications and operating systems (including Linux). The 32 to 64 bit transition is not helping, more cores and less clock speed is making it even worse. And this is true going backward as well for the same reason.
(2) Bank on your binaries failing or crashing. Sometimes you get lucky, most of the time you dont. There are new instructions yes, and to support them would probably mean trap for an undefined instruction and have a software emulation of that instruction which would be horribly slow and the lack of demand for it means it is probably not well done or just not there. Optimization can use new instructions but more than that the bulk of the optimization that I am guessing you are talking about has to do with reordering the instructions so that the various pipelines do not stall. So you arrange them to be fast on one generation processor they will be slower on another because in the x86 family the cores change too much. AMD had a good run there for a while as they would make the same code just run faster instead of trying to invent new processors that eventually would be faster when the software caught up. No longer true both amd and intel are struggling to just keep chips running without crashing.
(3) Generally, yes. For example gcc is a horrible compiler, one size fits all fits no one well, it can never and will never be any good at optimizing. For example gcc 4.x code is slower on gcc 3.x code for the same processor (yes all of this is subjective, it all depends on the specific application being compiled). The in house compilers I have used were leaps and bounds ahead of the cheap or free ones (I am not limiting myself to x86 here). Are they worth the price though? That is the question.
In general because of the horrible new programming languages and gobs of memory, storage, layers of caching, software engineering skills are at an all time low. Which means the pool of engineers capable of making a good compiler much less a good optimizing compiler decreases with time, this has been going on for at least 10 years. So even the in house compilers are degrading with time, or they just have their employees to work on and contribute to the open source tools instead having an in house tool. Also the tools the hardware engineers use are degrading for the same reason, so we now have processors that we hope to just run without crashing and not so much try to optimize for. There are so many bugs and chip variations that most of the compiler work is avoiding the bugs. Bottom line, gcc has singlehandedly destroyed the compiler world.
(4) See (2) above. Don't bank on it. Your operating system that you want to run this on will likely not install on the older processor anyway, saving you the pain. For the same reason that the binaries optimized for your pentium III ran slower on your Pentium 4 and vice versa. Code written to work well on multi core processors will run slower on single core processors than if you had optimized the same application for a single core processor.
The root of the problem is the x86 instruction set is dreadful. So many far superior instructions sets have come along that do not require hardware tricks to make them faster every generation. But the wintel machine created two monopolies and the others couldnt penetrate the market. My friends keep reminding me that these x86 machines are microcoded such that you really dont see the instruction set inside. Which angers me even more that the horrible isa is just an interpretation layer. It is kinda like using Java. The problems you have outlined in your questions will continue so long as intel stays on top, if the replacement does not become the monopoly then we will be stuck forever in the Java model where you are one side or the other of a common denominator, either you emulate the common platform on your specific hardware, or you are writing apps and compiling to the common platform.