[RPG] Will both Mage Slayer and Sentinel together reduce an enethe’s speed to 0

Yes, because cantrips are spells, per 5e SRD - Spellcasting:

Cantrips

A cantrip is a spell that can be cast at will, without using a spell slot and without being prepared in advance. Repeated practice has fixed the spell in the caster’s mind and infused the caster with the magic needed to produce the effect over and over. A cantrip’s spell level is 0.

(Emphases mine)

You only need to ask, "has the creature cast a spell?"

If you answer yes, you can use your reaction to make a melee weapon attack against that creature.

If the wording specified a spell of level one or higher, then cantrips would not trigger the reaction.

No, the Mage Slayer's attack takes place after the spell has been cast. From the DMG, page 252:

If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action.

Since the trigger for Mage Slayer is when a creature casts a spell, the reaction will take place after a creature casts a spell, not as creature casts a spell.

Note that Jeremy Crawford, lead rules designer, said the same thing in his unofficial ruling.