1st ability pointer table - table to 'Job Levels' (not important)
Job Levels:
Job levels: 3 bytes
0 ABP low
1 ABP high
2 [Ability] That is a table that has ABP requirement & Ability that can be learned for different jobs
Actions:
That is one of the beauty of FFV (from dev perspective). Instead of hardcoding what to do in each situation, FFV uses actions (8 byte structure) that have parameterize couple of pre-coded possibilities. Here and in most resources on the net these possibilities are called 'Damage Formula' ... wrong name because these 'formulas' are not used just for damage, but healing and other non-dmg actions (like change row, inflicting status, ...).
If you check my FFV Viewer they are under 'Magic' tab (wrong name I know, but it started with parsing actions, inflicted by magic).
Some of the command abilities are implemented with Actions (not all). There is a table that say what action (8 byte) will be used on specific command (ability). For example, when you choose 'Row' command, there is acttion for it and instead of hardcoding, the action contain reference to 'Row' formula, which has params to swap, to make you in front, in back,.... You may observe it in my Viewer - command actions are at the end of the list (Magic).
Innate ability effects:
That is similar to Job Innates. When you set a Job, you receive jobs innates. When you add support ability you add it innate too. For example a 'Knight' comes with Cover & Dbl Grip. If you put Counter on its free slot, the knight will get Counter innate too. From dev perspective innates are just set of bits that are checked in specific situations :)