So, at the start of a conflict, each player draws 5 cards and is allowed to use a

maximum of 3, of the 5 cards, for the entire.

What happens when, for example one of the Eldar Lv3 combat upgrade cards (I forget which one, I'm at work), allows a player to draw an extra card and use it's armour and offensive stats (not it's ability)... Technically, one could even stack these draw extra cards to draw up to 3 cards in a single combat round i.e.

You play the draw extra combat card and only use it's offensive and defensive stats. Then you play another one of the same card, and finally a different card to total 3 cards in one round.

Should the combat last 3 rounds, you could technically play up to 5 cards for said combat.

So, does the 3 card limit only apply when you're playing a combat card with it's abilities included or does it include a card played, simply for it's stats?

You would indeed get to use all 5 cards in your hand if you played Command of the Autarch twice in a battle. The limit only applies to playing 1 card in each of the combat iterations. If the card tells you to break one of the core rules (like adding another card), then you can do it.

However the Command of the Autarch card doesn't have any combat icons on it, so in effect you would still only have 3 cards' worth of icons in the battle, and 3 cards worth of abilities (2 of which are the CotA, not incredibly powerful effects).

There is at least one other card (Psychic Lance) which can force the enemy to lose an upturned card, so it is also possible to end up with less than 3 cards.