This is how I read the data sheet.
There are three general-purpose TC blocks each of which has 3 16-bit TCs. So that's a total of 9 16-bit TCs.
Within each block you can gang the timers in series so you could have 1 32- and 1 16-bit, or 1 48-bit TC in each block.
There is also the SysTick counter, this should be used for regular interrupts like the millis(), if it's not the entire Arduino team need shooting.
Then there's the RTT, this can be used to count elapsed seconds.
Then there's the 8 channels of PWM timers.
And finally there's the RTC which does all the things you'd expect of an RTC.
Or does it just have the 4 that the Cortex provides
Most timers are manufacturer-supplied peripherals and therefore nothing to do with the Cortex, of the above I think the only "Cortex timer" is SysTick.