Like title says. I'm working on a project where I'm messing with the timers, but need i2c (and possibly SPI) to work. Are any of the three timers used by these peripherals, or is it all done in other hardware?.
My understanding is that the serial UART doesn't rely on the timers, but I've not found a definitive answer on the other protocols.
The UART, I2C, SPI, Timers, ADC are all in hardware and they don't need each other.
Sometimes libraries use hardware timers. That is sometimes well documented and sometimes you have to read the source of the library. For some common libraries there are alternatives that use an other timer or no timer at all.
There are also modules that put the specific timing on that module. For example a module with many PWM outputs or a motor controller, or a serial smart display, and so on.
For normal timing in a sketch, you can use millis(). The Arduino is not like normal embedded systems. The use of interrupts and timers can often be avoided.
What I'm saying is this: There are many options. If you tell us about your project, maybe we can tell what the possibilities are.