Do slotless racial spells improve at higher character levels?

Question

The drow

When you reach 3rd level, you can cast the faerie fire spell once per day. When you reach 5th level, you can also cast the darkness spell once per day. Charisma is your spellcasting abilily for these spells.

Faerie fire is a 1st level spell and darkness 2nd level.

A typical magic user knows first level spells at first level and second level spells at 3rd level.

Since a drow can’t learn these spells until reaching 3rd and 5th levels, would these spells adjust to a higher level just like if a wizard would adjust there spells to a higher spell slot?

Answer 1

There is no difference in the text of a spell when you cast with a racial feature and they are cast at lowest level.

WHAT LEVEL IS A SPELL IF YOU CAST IT WITHOUT A SPELL SLOT? Such a spell is cast at its lowest possible level, which is the level that appears near the top of its description.

Spells are only scaled to a higher level when cast with a higher spell slot (PHB 201). The effect only changes if the spell's description specifically says so (i.e. a Darkness spell cast with a 3rd level spell slot still only dispels 2nd level spell). See here

Can you cast darkness with a higher level slot to end a spell of 3rd level or higher that creates light? No. The darkness spell can dispel only a light-creating spell of 2nd level or lower, no matter what spell slot is used for darkness. Similarly, the daylight spell can dispel only a darkness-creating spell of 3rd level or lower, regardless of the spell slot used.

Added note: the only racial spells that scale don't use spell slots to do so and are certain cantrips like the ones you could get from the High Elf Cantrip feature (PHB 24). Some include Fire Bolt (242) and Poison Spray (266) which include text "The spells damage increases... when you reach 5th level..." This is based on your character level so these spells would scale.

For your specific case, drow do not get any of these spells.

Answer 2

These particular spells do not scale at higher spell slots. Thus, it does not matter what level your Drow is (or what slot any caster using these spells uses, in fact).

Some spells simply do not have added benefits when cast at a higher spell slot. A spell only scales up with level when the spell description says it does. This is always indicated by a final section in the spell's description, headed in bold by at higher levels.

Had the game designers chosen different spells for the Drow racial ability, ones which scale with level, then you certainly would have seen some language specifying what effective level they are cast at.