3, with the combination you mentioned

With Race/Class/Feat/Magic Item combos, it is relatively simple to rack up Resistance to an absurd range of damage types. But in terms of nothing but Race and Feat...

First place goes to a Tiefling with the Infernal Constitution Feat for 3 resistances

Second place goes to the Volo's Guide Aasimar with 2 resistances

Third Place is shared by Dwarves, Stout Halflings, Tieflings (without the UA Feat), Tritons, and Dragonborn with one resistance each

The Arcane Savant can do this.

The Arcane Savant is a prestige class that focuses on getting the most from magic items.

At 3rd level, they can use their caster level on spells they cast using scrolls and wands.

Scroll Master (Su)

At 3rd level, an arcane savant can use his own caster level instead of the item’s caster level when using a scroll or other spell-completion item.

Since the Arcane Savant prestige class requires 5 hit dice as part of its prerequisites, the earliest a character can gain the Scroll Master ability is at 8 hit dice. This is faster than the Magician bard archetype, who gains a similar benefit at 10 (or more) hit dice.

At 10th level, the Arcane Savant gains their capstone ability, and can use their caster level for any single magic item.

Item Master (Su)

At 10th level, an arcane savant can spend an hour focusing his energies on a single non-charged magic item that requires an action to activate. At the end of this hour, that item becomes attuned to the arcane savant, and from that point on, that specific item can use the arcane savant’s caster level to resolve its effects rather than the item’s caster level. An arcane savant can change which item is attuned to him by repeating the attunement ritual, but he loses attunement to the previous item. An arcane savant can have only one item attuned to him at a time.

Note that the Arcane Savant is behind one caster level, although you can use the Magical Knack trait to compensate. So if you multiclass Wizard 5 / Arcane Savant 10, then you could use a Mask of the Skull's effects at 15th level, as you described.