[RPG] Do lower level spells work against high level spellcasters

Proficiency Bonus is not added to damage rolls.

Proficiency bonus is added to attack rolls, ability checks, and saving throws for which you are proficient. Damage rolls will add the appropriate modifier for the stat which was used to make the attack. However many spells, especially cantrips, do not add your casting mod to the damage.

There are some class abilities that allow proficiency to be added to damage rolls, but those are a specific exception rather than the general rule.

Firebolt requires you roll 1d20+INT+proficiency vs. AC and deals 1d10 damage

Make a ranged spell attack against the target. On a hit, the target takes 1d10 fire damage. A flammable object hit by this spell ignites if it isn't being worn or carried. - PHB p. 242

“Spell attack” = roll a d20 and add prof and mod. Spell save means target rolls defense.

Each spell's description indicates whether you need to make an attack roll, or the target needs to make a saving throw, or both.

Saving Throws

Many spells specify that a target can make a saving throw to avoid some or all of a spell’s effects. The spell specifies the ability that the target uses for the save and what happens on a success or failure. The DC to resist one of your spells equals 8 + your spellcasting ability modifier + your proficiency bonus + any special modifiers.

Attack Rolls

Some spells require the caster to make an attack roll to determine whether the spell effect hits the intended target. Your attack bonus with a spell attack equals your spellcasting ability modifier + your proficiency bonus. Most spells that require attack rolls involve ranged attacks. Remember that you have disadvantage on a ranged attack roll if you are within 5 feet of a hostile creature that can see you and that isn’t incapacitated (see chapter 9). - PHB p. 205

There are two types of attack spells requiring d20 rolls: melee attack spells and ranged attack spells.

The difference is that melee attack spells will not be made at disadvantage when next to an enemy combatant whereas ranged spells would be (and all ranged attacks for that matter).

The highest level spell I could find that uses a melee spell attack to deal damage is Mordenkainen's Sword (level 7). The relevant part of the spell reads:

When the sword appears, you make a melee spell attack against a target of your choice within 5 feet of the sword. On a hit. the target takes 3d10 force damage. Until the spell ends, you can use a bonus action on each of your turns to move the sword up to 20 feet to a spot you can see and repeat this attack against the same target or a different one.

However, it's worth noting that Plane Shift (level 7) requires a spell attack and a save to let you banish an enemy, which is equivalent to killing them most of the time:

You can use this spell to banish an unwilling creature to another plane. Choose a creature within your reach and make a melee spell Attack against it. On a hit, the creature must make a Charisma saving throw. If the creature fails the save, it is transported to a random location on the plane of existence you specify.

Otherwise, for a wizard, there aren't really spells that start at high level that require an attack roll.