Your Attack Bonus with a weapon consists of your Ability Modifier + your Proficiency Bonus (if you are proficient with that weapon). So the Attack Bonus you are looking at on the sheet is the result of the calculation, included to save you working it out every time, not part of it.
Firstly, yes, if a spell requires an attack, that attack still counts as an attack.
So, what you have to remember is the "specific beats general" rule. This is detailed on page 7 of the PHB. The core of the rule is:
If a specific rule contradicts a general rule, the specific rule wins.
So the general rule here is that familiars can't attack. There are 2 exceptions to this general rule:
A familiar can deliver spells with a range of touch on your behalf, even if the spell requires an attack roll.
A Warlock with the Pact of the Chain can forgo one of their attacks to let their familiar make one.
So when you cast a spell with a range of touch, you can have your familiar do the actual "touching" on your behalf. You cast the spell as normal using whatever actions it requires. The familiar is required to use their reaction, and if the spell requires an attack roll, it makes the attack roll. Since it uses your modifier anyway, it's exactly the same as you making the attack roll except that you don't have to stand next to what you're casting the spell on.
In the case of a Warlock with the Pact of the Chain, the Warlock takes the Attack action as usual, then has the familiar do the actual attack. The errata for the PHB says:
When you
let your familiar attack, it does so with its
reaction.
If the Warlock can make multiple attacks with the Attack action, the familiar can use its reaction to replace one of them with its own attack, then the Warlock makes the rest.
Finally, only spells with a range of touch can be delivered by your familiar. There is no option for having your familiar cast a spell on your behalf, and the option for allowing a familiar to attack instead of yourself specifically says "when you take the Attack action", not just "when you make an attack".
Best Answer
For cantrips and other spells, both the spell save DC and spell attack modifier include proficiency bonus.
If you check the sorcerer's Spellcasting rules, it tells you how to calculate your spell save DC and your spell attack modifier.
Your character's proficiency bonus is included in both formulas.
Cantrips are spells. When you make an attack roll as part of a sorcerer spell, then it's a spell attack, so you roll a d20 and add your Spell attack modifier, comparing the total versus their AC. However, the proficiency bonus is not usually included in damage rolls.
Similarly, if a sorcerer spell requires the target to make a saving throw, then the target would roll their saving throw (d20 + some modifiers) against your spell save DC.