Q:

How can the Microcontroller run anything else if the interrupt is really fast?

just a quick question. I am just confused how you are suppose to run anything else if you have a periodic interrupt going off every X amount of seconds.
If I have an ADC being interrupted at 38kHz or about ~26uS how does that leave room  to do anything? Let say I want the ADC to still be triggered every 26uS but I also want to do some math that uses the output of the ADC. Would that mean I need to create another interrupt that execute after the 26uS mark but it needs to finish before the next ADC trigger?
This is assuming the ISR for the ADC as soon as it triggers, its completed.
The way I think of this is a time line of deadlines
If I have an ADC that triggers every 26uS then:
0....26uS....52uS....78uS
Then the task that I want to do math in would need to finish in between the ADC triggers?
0....26uS...[Math Task]...52uS...[Math Task]....78uS
and if I want to write another task along side my math one it would be like this?
0....26uS[New Task][Math Task]....52uS..[New Task][Math Task]....78uS.
So in essence if you want to run anything else, does it need to be faster then your biggest (slowest) interrupt frequency? 
Is it viable just to write your task in terms of interrupts and have it in a timeline like above or would you use the while(1) loop etc. Not sure how the while(1) loop would even work when it comes to deadlines. 
Too me this seems crazy, What if I want to do audio processing? Sampling an audio signal at 44kHz and implement a digital filter by feeding my ADC values into my difference equation.
Would that mean my digital filter algorithm task: 

needs to be faster than 44kHz?
What if its never possible for my digital filter to be that fast due
to the arithmetic and storing past values and what not?
Would it be not implementable then?
How do people like Sonos have MCU doing audio processing and stuff?

EDIT: Taking your suggestions into account I picked up 3 micro controllers for further play testing: Let me know what you guys think.
- PIC18F25K83 
- dsPIC33EP64GP502
- STM32L432KC

A:

Short answer is, it can't run anything else if the interrups keep interrupting the normal execution flow. There are MCUs that run main code for one or two opcodes before accepting a new interrupt, and there are MCUs that don't exit the interrupt context at all if next interrupt is pending.
Executing and returning from interrupt takes some time too, so obviously interrupts can't happen faster than this overhead plus the actual execution time of the interrupt routine. Either you need a faster MCU then to allow more interrupts per second, or slowe interrupt rate to process them.
So yes, as you said yourself, this is crazy, and that is why audio processing is not made in ADC interrupt one sample at a time. If you are limited to this, you have the wrong MCU for audio processing. The idea of loop you mentioned is kind of towards the right way because it does not use interrupts, you have more time to fecth and calculate each sample as there is no context switch. MCUs that support DMA go further than this, the CPU can do other things while samples get written to memory without CPU. The DMA controller can be configured to give you an interrupt after a certain amount of samples have been transferred so you can process it in blocks, maybe not in interrupt context but when you have a time slot for it.
How does some commercial speaker do it? Not with a 8-bit AVR that is for sure. It might have a multi-GHz multi-core SoC with a built-in audio processor or a dedicated DSP.

