In both cases, where Rona says "nonland cards exiled with Rona", it means only nonland cards in exile that were put there due to Rona's first or third abilities, and not to cards exiled due to any other ability (including those of Deadeye Tracker or of Agent of Erebos) or by any other means (C.R. 607.2a, 607.4). See also this thread. Thus the answer to your questions is: no.
EDIT: Correction after comment 3 was posted.
EDIT (Dec. 26): Added rule citation.
No, that doesn't work. Rona has what's called linked ablities. The second ability is linked to the first, and the second abilty is also linked to the third. This means, that the second ability can only access cards exiled with the other two abilities, but not cards somehow exiled by the same permanent with some other ability. A copy of Rona will also copy those linked abilities and they will likewise be linked, even if it is now Lazav that has those abilities.
Furthermore, since Lazav can switch to being something else and then revert to Rona, all cards exiled from his previous incarnation as Rona cannot be accessed anymore, because those cards were exiled by different instances of those abilities, which aren't linked to the new instance of the second ability. To make matters worse, even if Lazav copies Rona while being a copy of Rona already, that link is still broken.
For example what if there was a card that gave Rona, Disciple of Gix and additional ability to exile cards. Can't think of something off the top of my head, but lets assume you were able to add some extra text to her, like "1, Exile an instant or sorcery card from your graveyard."
Would this new ability be linked to her playing cards from exile ability?
607.1. An object may have two abilities printed on it such that one of them causes actions to be taken or objects or players to be affected and the other one directly refers to those actions, objects, or players. If so, these two abilities are linked: the second refers only to actions that were taken or objects or players that were affected by the first, and not by any other ability.
607.1a An ability printed on an object within another ability that grants that ability to that object is considered to be “printed on” that object for these purposes.
607.1b An ability printed on either face of a double-faced card (see rule 711) is considered to be “printed on” that object for these purposes, regardless of which face is up.
607.1c An ability printed on an object that fulfills both criteria described in rule 607.1 is linked to itself.
Note, that the rule talks about abilities printed on the card, so granting a new ability to an object with linked abilities will not make that new ability linked to the original ones.
The CR then goes on about different kinds of linked abilities, the first item on the list is where Rona falls in:
607.2. There are different kinds of linked abilities.
607.2a If an object has an activated or triggered ability printed on it that instructs a player to exile one or more cards and an ability printed on it that refers either to “the exiled cards” or to cards “exiled with [this object],” these abilities are linked. The second ability refers only to cards in the exile zone that were put there as a result of an instruction to exile them in the first ability.
I have Lazav, the Multifarious in play.
I have Rona, Disciple of Gix, Deadeye Tracker, Agent of Erebos in my graveyard.
I make Lazav, the Multifarious the Deadeye Tracker, and then proceed to exile some cards from opponents graveyard.
Can I then make Lazav, the Multifarious the Rona, Disciple of Gix and play those cards from exile?
Same with Lazav, the Multifarious copying Agent of Erebos and then playing an enchantment. Then making him Rona, Disciple of Gix?
Essentially are the cards exile "stamped" with his name, and allowing for these types of interactions?
Niv-Mizzet Reborn
Feather, the Redeemed
Estrid, the Masked
Teshar
Tymna/Ravos
Najeela, Blade-Blossom
Firesong & Sunspeaker
Zur the Enchanter
Lazav, the Multifarious
Ishai+Reyhan
Click images for decks->
-Prime Speaker Vannifar
---------------------Will & Rowan Kenrith
EDIT: Correction after comment 3 was posted.
EDIT (Dec. 26): Added rule citation.
Furthermore, since Lazav can switch to being something else and then revert to Rona, all cards exiled from his previous incarnation as Rona cannot be accessed anymore, because those cards were exiled by different instances of those abilities, which aren't linked to the new instance of the second ability. To make matters worse, even if Lazav copies Rona while being a copy of Rona already, that link is still broken.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)
For example what if there was a card that gave Rona, Disciple of Gix and additional ability to exile cards. Can't think of something off the top of my head, but lets assume you were able to add some extra text to her, like "1, Exile an instant or sorcery card from your graveyard."
Would this new ability be linked to her playing cards from exile ability?
Niv-Mizzet Reborn
Feather, the Redeemed
Estrid, the Masked
Teshar
Tymna/Ravos
Najeela, Blade-Blossom
Firesong & Sunspeaker
Zur the Enchanter
Lazav, the Multifarious
Ishai+Reyhan
Click images for decks->
-Prime Speaker Vannifar
---------------------Will & Rowan Kenrith
Note, that the rule talks about abilities printed on the card, so granting a new ability to an object with linked abilities will not make that new ability linked to the original ones.
The CR then goes on about different kinds of linked abilities, the first item on the list is where Rona falls in:
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)