It does combine
First, let's pose this question:
Can you combine Vampiric Touch and Touch of Death on the same attack?
I had initially thought it did not, because Vampiric Touch is a melee spell attack. However, the PHB states on page 195 about melee and ranged attacks
Many spells also involve making a ranged attack
When you make a ranged attack with a weapon, a spell, or some other means...
and
A melee attack typically uses a handheld weapon such as a sword.....a few spells also involve making a melee attack.
From the lack of distinction made between spell attacks and regular attacks, we can say that Vampiric Touch counts as a melee attack for the purposes of activating Touch of Death. So...
Does Touch of Death activate Vampiric Touch?
Vampiric Touch states that you "regain hit points equal to half the amount of necrotic damage dealt". It does NOT say that you regain hit points based on the damage of this spell but rather implies damage dealt by the attack itself. You can consider Touch of Death's extra damage as applying to the melee spell attack. This works specifically because you deal necrotic damage, and the spell is sure to specify that it only heals on necrotic damage dealt. We can infer that the designers anticipated stacking melee attacks like this and wanted only necrotic to interact with the healing effect.
Thus, as a 5th level Death Cleric, you combine the two to deal 3d6 necrotic plus 15 necrotic, healing for half the total damage.
By this logic, you cannot stack your Divine Strike onto Vampiric Touch's healing, because it specifically requires a weapon attack.
It should also be noted that touch of death works with any melee spell attack, but not ranged spell attacks made on adjacent enemies.
Remember that doing this requires your DM to accept that spell attacks are the same as regular attacks for the purposes of activating Touch of Death, and that all necrotic damage applies to Vampiric Touch for healing, not just the spell itself. If one of those is an issue to your DM, you cannot combine them for healing.
More definitive proof
Thanks to Airatome for finding this tweet to Mike Mearls about this.
Asker: Death domain cleric, use vampiric touch and death touch together. Health back from VT or both?
Mike Mearls: I'd say both - both require you to spend a resource, different effects. Stacking same spell/ability is not allowed, 2 diff is ok.
remember that DM always had final say
See also: How does Vampiric Touch interact with Resistance/Vulnerability?
No.
As others have noted, if Blessed Healer were triggered by Goodberry, it would happen when you cast the spell and not when one of the berries is consumed.
However, casting Goodberry does not satisfy the trigger for Blessed Healer: "When you cast a spell...that restores hit points to a creature other than you". This is because, at the time that you cast the spell, it is possible that you yourself could eat all of the berries, or that no one eats them before they lose their potency.
Strictly speaking, when you cast Goodberry, it has yet to be seen whether it will restore hit points to a creature other than you. But Blessed Healer either triggers at that moment or not at all.
At the gaming table it might look like this:
Player: "I cast Goodberry. Does that trigger my Blessed Healer?"
DM: "When you cast it, did it restore hit points to a creature other than you?"
Player: "No..."
DM: "Then there's your answer."
Best Answer
Yes, this should work. Disciple of Life says that
Vampiric Touch is a spell of 1st level or higher, check. You are a creature, so if you use Vampiric Touch to restore your hit points, you should get the benefit.