Almost. You can cast both halves of a card with fuse only if it's in your hand (C.R. 702.101a). Therefore, while you can cast both halves of Breaking & Entering with Kari Zev's Expertise, since you do so from your hand, you can cast only one half of that card with Goblin Dark-Dwellers's ability, since you do so from your graveyard (C.R. 708.2a). Note also that:
You can target Breaking & Entering in the graveyard with that ability because that card goes to the graveyard as the last step of resolving, before Goblin Dark-Dwellers's ability goes on the stack [C.R. 608.2k, 116.3b, 116.5].
The Breaking half requires a target, which you must choose if you cast that half or both halves of Breaking & Entering (C.R. 601.2c, 702.101b).
EDIT (Nov. 20): See comment 4.
EDIT (Oct. 1, 2019): See comment 5. Edited note from Nov. 20.
With the release of Amonkhet, the answer to comment 1 has changed. Neither Kari Zev's Expertise nor the triggered ability of Goblin Dark-Dwellers lets you cast Breaking & Entering, since in either case, Breaking & Entering has converted mana cost 8, which exceeds the converted mana cost required for Kari Zev's Expertise or that ability. In each case, "cast[ing] a card" from the hand or graveyard, respectively, is referred to, rather than casting a spell (compare C.R. 109.2a with C.R. 109.2b), so what's relevant here is the converted mana cost of the card in the hand or graveyard, respectively (not the converted mana cost of the spell it will become), which will beIn general, a split card's converted mana cost, while it's not on the stack, is the total converted mana cost of both halves since "[t]he mana cost of a split card is the combined mana costs of its two halves" (C.R. 708.4, 708.4b, 202.3). See also this thread.
EDIT (May 27, 2019): Correctness edit.
EDIT (Oct. 1, 2019): See comment 5.
EDIT (Oct. 1, 2019): Edited after comment 6 was posted.
EDIT (Jan. 20, 2020): Edited slightly.
As of Throne of Eldraine, the answer to comment 1 has had some changes.
When that set is released (and in prereleases), for the purposes of determining whether you can cast a split card from your hand with Kari Zev's Expertise or from your graveyard with the triggered ability of Goblin Dark-Dwellers, what is relevant are the characteristics of the half you choose (or, if the card is in your hand and has fuse, and you so choose, the characteristics of both halves) in that zone before you begin to cast that card (new C.R. 601.3e; C.R. 708.3a, 702.101a); in each case, "cast[ing] a card" from the hand or graveyard, respectively, is referred to, rather than casting a spell (compare C.R. 109.2a with C.R. 109.2b), so the characteristics of the corresponding spell are irrelevant.
When that set is released (and in prereleases), with Kari Zev's Expertise or Goblin Dark-Dwellers's triggered ability, you can cast from the corresponding zonefrom your hand the Breaking half (converted mana cost 2), but not the Entering half (converted mana cost 6) and not both halves (both because it has converted mana cost 8 and, for the latter ability, because it's not in your hand [C.R. 702.101a]converted mana cost 8) (C.R. 708.4, 708.4b, 202.3).
EDIT: Correction and added rule citations after comment 6 was posted.
Dark-Dwellers doesn't change. It requires a target and Split cards still have a combined mana cost in any zone but the stack. While you can cast Breaking off of an Expertise, you still can't target only that half of the split card with the Goblin. You target the card as a whole which still has a CMC of 8 which means it is not a legal target.
Need advice.
Would this combo work?
Kari Zev's Expertise into Breaking // Entering then grab Goblin Dark-Dwellers and do Breaking // Entering again?
Almost.You can cast both halves of a card with fuse only if it's in your hand (C.R. 702.101a).Therefore, while you can cast both halves of Breaking & Entering with Kari Zev's Expertise, since you do so from your hand, you can cast only one half of that card with Goblin Dark-Dwellers's ability, since you do so from your graveyard (C.R. 708.2a).Note also that:You can target Breaking & Entering in the graveyard with that ability because that card goes to the graveyard as the last step of resolving, before Goblin Dark-Dwellers's ability goes on the stack [C.R. 608.2k, 116.3b, 116.5].EDIT (Nov. 20): See comment 4.
EDIT (Oct. 1, 2019): See comment 5. Edited note from Nov. 20.
With the release of Amonkhet, the answer to comment 1 has changed. Neither Kari Zev's Expertise nor the triggered ability of Goblin Dark-Dwellers lets you cast Breaking & Entering, since in either case, Breaking & Entering has converted mana cost 8, which exceeds the converted mana cost required for Kari Zev's Expertise or that ability. In each case, "cast[ing] a card" from the hand or graveyard, respectively, is referred to, rather than casting a spell (compare C.R. 109.2a with C.R. 109.2b), so what's relevant here is the converted mana cost of the card in the hand or graveyard, respectively (not the converted mana cost of the spell it will become), which will beIn general, a split card's converted mana cost, while it's not on the stack, is the total converted mana cost of both halves since "[t]he mana cost of a split card is the combined mana costs of its two halves" (C.R. 708.4, 708.4b, 202.3).See also this thread.EDIT (May 27, 2019): Correctness edit.
EDIT (Oct. 1, 2019): See comment 5.
EDIT (Oct. 1, 2019): Edited after comment 6 was posted.
EDIT (Jan. 20, 2020): Edited slightly.
When that set is released (and in prereleases), for the purposes of determining whether you can cast a split card from your hand with Kari Zev's Expertise
or from your graveyard with the triggered ability of Goblin Dark-Dwellers, what is relevant are the characteristics of the half you choose (or, if the card is in your hand and has fuse, and you so choose, the characteristics of both halves) in that zone before you begin to cast that card (new C.R. 601.3e; C.R. 708.3a, 702.101a);in each case, "cast[ing] a card" from the handor graveyard, respectively, is referred to, rather than casting a spell (compare C.R. 109.2a with C.R. 109.2b), so the characteristics of the corresponding spell are irrelevant.When that set is released (and in prereleases), with Kari Zev's Expertise
or Goblin Dark-Dwellers's triggered ability, you can castfrom the corresponding zonefrom your hand the Breaking half (converted mana cost 2), but not the Entering half (converted mana cost 6) and not both halves (both because it has converted mana cost 8 and, for the latter ability, because it's not in your hand [C.R. 702.101a]converted mana cost 8) (C.R. 708.4, 708.4b, 202.3).EDIT: Correction and added rule citations after comment 6 was posted.