Nate - this is a long, and company specific conversation, but I’ll try to cover it at a high level. There is documentation on all of this in the ERP docs, but this is a fairly universal and abundant data can be found on Cycle Counting and inventory concepts on the internet.
ABC - is a method of classifying inventory value into schedulable cycles for counting. Your usage completely depends on how you value inventory. Generally someone will put the parts that make up 80% of the value inventory (not the count/qty) in the A group and cycle count them often. Then you split the next 20% of value into B and C and count them less frequently.
Up to Date inventory - Sure it can, but it takes more discipline than is found in 99% of the shops out there. Inventory is inevitable fouled by forces outside of the standard receive/issue, produce/ship, inspect/reject/accept transactions Cycle counting is an alternative to doing a full physical, but is often used in conjunction with a full physical. Talk to your accountants about ‘inventory expense’ adjustments and why they never look good to auditors. This will explain more about the WHY than the HOW but you’ll learn a lot about the financial side of inventory.
Who counts? Everyone. Everyone but the guys in charge of inventory. This is a General Accounting Principles (GAP) practice of ‘checking the checkers’ - auditing the inventory - and it’s usually by those whose job is not affected by the count (so the counting is true, in contrast to someone ‘adjusting the count’ to match the Inventory QOH report - a big NO NO). Again, talk to your accounting/auditing team for more rationale.
Hope that starts you off on the right path. 