Dimir Doppelganger becoming Lazav, Dimir Mastermind

Question

I have a few clarification questions regarding what happens after I use the activated ability of Dimir Doppelganger to target a Lazav, Dimir Mastermind that's sitting in a graveyard. For simplicity, I assume that the only card in play before the ability resolves is the Dimir Doppelganger, which has never used it's ability before.

Firstly, am I correct in saying that the card I have on the battlefield after resolution, in effect, has the name Lazav, Dimir Mastermind, is of the type Legendary Creature - Shapeshifter, and has card text which reads:

Hexproof

Whenever a creature card is put into an opponent's graveyard from anywhere, you may have Lazav, Dimir Mastermind become a copy of that card except its name is still Lazav, Dimir Mastermind, it's legendary in addition to its other types, and it gains hexproof and this ability.

1{U}{B}: Exile target creature card from a graveyard. Lazav, Dimir Mastermind becomes a copy of that card and gains this ability.

Assuming this is correct, and I use the activated ability again to target another creature in a graveyard -- let's say Grizzly Bears -- then the card I have in play is now named Grizzly Bears, of type Creature - Bear and has only the activated ability of the original doppelganger (losing hexproof and the triggered ability of Lazav.)

And finally, if I instead choose to use the triggered ability my doppel-Lazav in response to a creature entering an opponent's graveyard -- we can assume it's Grizzly Bears again -- then my card now named Lazav, Dimir Mastermind, of type Legendary Creature - Bear and reads:

Hexproof

Whenever a creature card is put into an opponent's graveyard from anywhere, you may have Lazav, Dimir Mastermind become a copy of that card except its name is still Lazav, Dimir Mastermind, it's legendary in addition to its other types, and it gains hexproof and this ability.

Answer 1

Assuming your grizzly bear scenarios are either/or (and you're not doing one after another)...

You are correct. The card will come back as either a Lazav copy or a Doppleganger copy and it depends entirely on which card's copy ability you use.

It's the ability itself (of either lazav or the doppleganger) that causes the copy to retain the previous abilities, because it uses the wording: "gains this ability."