Let's say I'm a human and decide to buy a cyberarm. My non-augmented agility and strength are both 3.
1) Can I take both the agility customization to boost the agility up to 6 and the agility enhancement of 3 to bring it up to 9? This seems to violate the limit of +4 to augmentation, but you're replacing your entire arm. How about if my agility was 5?
2) If I took improved agility at character creation, can I then choose to bring my agility up to 7 with customization?
3) I've also got this sweet Ares Alpha that I want to use with this new arm. In order to use this, would I need to coordinate both arms so that I only get to use the agility 3?
4) If the arm is alphaware, do the enhancements and implant weapons need to be alpha grade as well?
5) I'm an adept. Can I channel my focus through the ware and use my improved pistols with the arm?
Augmented Maximum does not, by developer intent & design, apply to Cyberarms. On the other hand, Cyberarms do not boost your inherent values, so they do not impact your movement rate and physical limit. You can have a Customized Cyberarm at any Strength or Agility value, but can only use it when it's not higher than your own natural maximum (which is modified by the exceptional attribute quality and racial modifications), before Enhancement.
Two-handed weapons, which people tend to rule as everything past SMGs (Assault Rifles, Longarms, Heavy Weapons), will average your two arms.
All accessories of cyberlimbs must be the same grade as the cyberlimb. The sole exception that I know of are implanted commlinks/cyberdecks, since with those you pay the grade-costs for the slot, not for the item.
If you pay for it with essence, it's part of you, so your abilities apply. This applies for vision enhancements and magical targeting, but I'd say it also applies to cyberlimbs, since they are still a part of you. Look at it this way, someone with 1 arm loses no essence, but someone with a cyberarm does. They themselves trade part of their soul to make that arm part of them.
A GM has every right to veto a character build that abuses cyberlimbs, I and some others put the line at your natural value (before racial mods) being < 3/ the Cyberlimb value after racial mods are subtracted. So for example for a Human that's an arm past 6 Agility when the character has 2, and for an Elf that'd be past 7 when the character has 3.