Spells – Does a level 1 wizard who casts the Frostbeam Cantrip deal 1d4 damage + spell modifier?

A level 1 wizard who throws a frostbite deals damage to 1d4 + its spell modifier.

As you have already noticed, a can trip is automatically raised to half the wizard's level and rounded up. A level 1 wizard can increase something to 0.5 * 1, rounded up. 0.5 * 1 = 1. Therefore, the Cantrip can only be cast as a level 1 spell (minimum level). As a level 1 spell, the Frostbite deals 1d4 damage plus its spell modifier.

Another way of thinking about it (but drawing the same conclusion) is that the Frostbeam is a Level 1 Cantrip. A can trip is magic. Given that the highest level spell location that your level 1 wizard has is level 1, there is no real way to increase the spell. The Cantrips page you linked to says it like this:

For a typical caster, this means that their level corresponds to the highest level of your magic slot.

dnd 5e – Can I use the Martial Arts feature to change the Kensei Shot's 1d4 into my martial arts dice?

Kensei weapons are monk weapons

Kensei weapons. Choose two types of weapons as your Kensei weapons: a melee weapon and a ranged weapon. (…) Weapons of the chosen type are for you monk weapons.

All rules that apply to monk weapons also apply to the weapons chosen by Kensei.

However, the damage of Kensei's shot is in addition to the normal damage of the weapon. You can not update it to use your combat cubeAs Martial Arts dies, it only replaces the normal damage of the weapon.