For those two abilities, you don't have to control either target.

Gaining control of a creature doesn't cause a player to gain control of any Auras or Equipment attached to it.

Removing lore counters won't cause a previous chapter ability to trigger. If lore counters are removed from a Saga, the appropriate chapter abilities will trigger again when the Saga receives more lore counters.

If one of the target permanents of the chapter I or chapter II ability is an illegal target as that ability resolves, the exchange won't happen. If both targets are illegal, the ability doesn't resolve.

If the same player controls both target permanents as the chapter I or chapter II ability resolves, nothing happens.

Each symbol on the left of a Saga's text box represents a chapter ability. A chapter ability is a triggered ability that triggers when a lore counter that is put on the Saga causes the number of lore counters on the Saga to become equal to or greater than the ability's chapter number. Chapter abilities are put onto the stack and may be responded to.

A chapter ability doesn't trigger if a lore counter is put on a Saga that already had a number of lore counters greater than or equal to that chapter's number. For example, the third lore counter put on a Saga causes the chapter III ability to trigger, but chapters I and II won't trigger again.

For the chapter II ability, either target can have card types the other does not. For example, you can target an artifact land and an artifact.

Once a chapter ability has triggered, the ability on the stack won't be affected if the Saga gains or loses counters, or if it leaves the battlefield.

As a Saga enters the battlefield, its controller puts a lore counter on it. As your precombat main phase begins (immediately after your draw step), you put another lore counter on each Saga you control. Putting a lore counter on a Saga in either of these ways doesn't use the stack.

If multiple chapter abilities trigger at the same time, their controller puts them on the stack in any order. If any of them require targets, those targets are chosen as you put the abilities on the stack, before any of those abilities resolve.

Once the number of lore counters on a Saga is greater than or equal to the greatest number among its chapter abilities, the Saga's controller sacrifices it as soon as its chapter ability has left the stack, most likely by resolving or being countered. This state-based action doesn't use the stack.