Stop... I know I told you to look at the big picture, but you can't hope to understand how to build a house without first learning how to use a hammer.
In Arcade games they don't use PIA RAM chips, the console buttons and encoder wheels/rollers go "DIRECT" to a RAM? or an interface circuit before RAM?
Don't bother with the PIA, it's use won't become clear until you understand more of what's going on with the rest of the circuit. By the way, PIA typically don't have RAM. I suppose they can, I just don't recall any that do.
When Looking at an arcade schematic how do you calculate/math formula to get the RAM's speed and Access time? and calculate the data buss frequency/time?
Understand that MHz is the frequency or the number of cycles per second. It's a function of time, but not time itself.
To figure out how long one cycle is at MHz in terms of ns, the formula is
T = 1000/MHz. Therefor, a 1MHz CPU has a cycle time of 1000ns. At 1.7MHz, that cycle time is ~588ns.
The CPU/MPU frequency sets the speed and access time for a RAM chip?
No, not always. Sort of. Not really. Depends on a number of factors that is outside of the scope of discussion I want to write about.
You also can't predetermine what the RAM access time should be just going off the CPU speed. That's actually a very poor indicator. You need to look at how the CPU uses the RAM. The 6502 is specifically designed to work with slower (translated to cheaper) RAM, unlike other chips of that era.
I suggest you understand something a little simpler, like the CPU itself. The 6502 is a blindingly simple and very nice to learn from. It's also an astonishingly good example to learn timing from since the Atari 2600 uses a variant known as the 6507. In my honest opinion, the 2600, with its very strong community and excellent software support, is probably the very best system to learn everything you could care to know about hardware timing. Not only would you be Racing the Beam you'll have to contend with the mis-matched clock rates of the 6507 and the T.I.A. The T.I.A. is like a beautiful 50's pin up. She'll give you tons of excitement, but she ain't going to cook you breakfast the next morning. Other 6502 based systems often use a better video interface, like your high school sweetheart after she gained 80lbs you want to settle in with who'll cook you breakfast but they're not very exciting in bed. The 6532 RIOT in the 2600 is like an older child. Enjoy
Do not ask questions about the 2600, Google it instead.
I won't do any more quotes, I have no time to fuss with this.
If you wish to understand why TTL sometimes cannot drive a CMOS circuit, you need to understand their differences first. This is why I told you to Google it.