Are LUTs hardcoded for the logical output they give? Like an AND LUT will only ever output the AND of its inputs? And is it possible to redirect the output of, for example, AND LUTs into something else like an OR or XOR LUT? What is the advantage of DSPs over programming an adder/multiplier in multiplexed LUTs?

I'm a bit confused what exactly a FPGA is doing that is so much more efficient than a normal CPU - is the idea that you're 'hardcoding' these lookup tables with your hardware language such that your logic is more streamlined?

@juliob this is correct – in an FPGA, your computation happens at the speed of electricity, rather than at the speed of your processor. Additionally, if you know the memory characteristics of your system (as is common for HW use cases) you can often use local buffers to store temporary results instead of doing expensive loads from memory.