I don't see why this wouldn't work, as nothing prevents you from taking a reaction on your turn.
Thus, the following sequence is valid:
- The wizard uses their action to Ready the shocking grasp spell,
which the familiar will deliver.
- The familiar uses part of its movement to move within touch range of
the target.
- The familiar uses its reaction to deliver the wizard's shocking
grasp spell. (The wizard also uses their reaction to use their
readied action.)
- The familiar uses its action to do something.
- The familiar completes its movement.
The only catch here is that the wizard's reaction is consumed, and they have to maintain concentration until that time.
But yes, the familiar cannot use a readied move if the wizard wants to use the familiar to deliver a touch-range spell, as both would need to use the familiar's reaction, and the familiar can only take one reaction.
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
Spells with a range of self cannot be cast via familiar
The restriction you quote acts exactly as it says: you can only cast touch-ranged spells through your familiar. "Self" != "touch," so you're out of luck.
As for touch spells that damage someone, you correctly got forbiddance, inflict wounds, and shocking grasp, but you missed symbol and glyph of warding. But they're strange edge-cases—the damage isn't done when the spell's cast, but rather when the glyph is triggered. There's also plane shift which, when cast on an unwilling target, is a spell attack which doesn't do any damage.
Magic stone—from the Elemental Evil Player's Companion—is another edge-case: you cast the spell on the stones via touch, but then make a ranged spell attack with them to damage someone.