Let's start with the basics...
Living creatures are healed by channeled positive energy used to heal living creatures and Cure spells. They are injured by channeled negative energy used to injure living creatures and Inflict spells.
Unliving creatures are healed by channeled negative energy used to heal unliving creatures and Inflict spells. They are injured by channeled positive energy used to injure unliving creatures and Cure spells.
Dhampir are "[t]he half-living children of vampires birthed by human females". Mechanically this has no effect, except for the following racial trait:
Negative Energy Affinity: Though a living creature, a dhampir reacts
to positive and negative energy as if it were undead—positive energy
harms it, while negative energy heals it.
This swaps them from the living set of conditions to the unliving set of conditions. RAW and RAI, Cure and Inflict spells will work as though the Dhampir were undead.
Undead creatures inherit the following racial trait from their creature type:
Cannot heal damage on its own if it has no Intelligence score,
although it can be healed. Negative energy (such as an inflict spell)
can heal undead creatures. The fast healing special quality works
regardless of the creature’s Intelligence score.
Negative energy heals them, with Inflict spells specifically called out as being negative energy.
Under Cure Wounds, the following text can be found:
Since undead are powered by negative energy, this spell deals damage to them instead of curing their wounds. An undead creature can apply Spell Resistance, and can attempt a Will save to take half damage.
Because Dhampir are treated as undead, Cure Light Wounds would injure them. Similar sources of magical healing would also injure them, though Celestial Healing and Infernal Healing work just fine. In fact, Dhampir are not even damaged by holy water itself since holy water is not based on positive energy and they are not undead. They are only treated as undead for a specific set of circumstances.
Life-Dominant Soul reads as follows:
Benefit: You are healed by channeled positive energy used to heal
living creatures and channeled negative energy used to heal undead,
but both only heal half the normal amount. You still take damage from
positive energy used to harm undead, such as that from channeled
energy and lay on hands.
This results in the following list of effects and the reaction your character has to them:
- Channeled positive energy used to heal the living heals you for half the normal amount.
- Channeled positive energy used to damage the undead deals full damage to you.
- Channeled negative energy used to heal the undead heals you for half the normal amount.
- Channeled negative energy used to damage the living has no effect.
Cure and Inflict spells, unlike channeled energy, have no "intent" component, so here is the RAW of what would happen:
- Cure spells treat you as if you are undead and damage you.
- Inflict spells treat you as if you are undead and heal you.
This makes little sense, so I recommend GMs use the following house rule interpretation of RAI to mirror Channel Energy:
- Cure spells used with intent to heal you heal you for half the normal amount.
- Cure spells used with intent to harm you harm you for the full amount.
- Inflict spells used with intent to heal you heal you for half the normal amount.
- Inflict spells used with intent to harm you have no effect.
If your GM likes the above interpretation of how this feat would interact with Cure and Inflict spells, then the feat makes you less effectively healed by any means, though able to be on the party's Wand of Cure Light Wounds medical insurance plan. I'd recommend chipping in twice the amount everyone else does to make up for twice the uses required to heal you.
If your GM does not, then you still need your own Wand of Inflict Light Wounds.
Specific Instances Requested
Dhampir clerics can channel positive energy to heal the living with no trouble, but should be VERY careful about channeling positive energy to harm the undead, even with the feat. Channeling negative energy is still a better option for them, since they can heal themselves and undead minions with the channeled negative energy, or damage any living around them without damaging themselves. The last effect is unique among negative energy clerics.
Dhampir bards using Cure Light Wounds on themselves should not.
Potions and scrolls work just like spells, therefore they will have the same effects as the spells they are based on.
The Silver Crane materials you linked do not mention any sort of positive energy or negative energy, and therefore function exactly as if the dhampir were living. Remember, they are only treated undead for the purposes of positive and negative energy, and the Silver Crane appears to channel a form of "divinely good" energy, not unlike a Paladin's Smite Evil ability, since it also harms evil outsiders.