Yes he should be able to cast his spells in this manner but with the following conditions. He must designate which spells he a memorized for that day. I usually use the spell point cost to let casters purchase their magic slots. I limit it to this degree. This is an example of a 20th level caster.
A 20th level wizard (for example) would have 89 levels of ...
Context is Important
First, you need to think about the time scale you are using. In my experience, most castings of sending do not happen "in combat and other fast-paced situations," and therefor, time is not even being marked by rounds or limited by actions. In this context, "immediately" simply means 'before the next event', whether ...
Unless defined in the rules, words have their natural English meaning.
Immediately means right now.
Within the context of a spell like Sending, it means that the reply comes during the caster's Cast A Spell action.
If you can see it, you can target it
Page 204 of the Player's Handbook, in the Spellcasting chapter, says:
To target something, you must have a clear path to it, so it can't be behind total cover.
That, to my mind, is what is meant by any spell description that says "a target you can see". You don't need to be able to read their facial expression ...
You can use Two-Handed weapons, including the Two-Hand trait, with HotA
You are able to wield your staff (or another weapon) in two hands while you cast Hand of the Apprentice.
Somatic requires that your hands are not bound.
You can use this component while holding something in your hand, but not if you are restrained or otherwise unable to gesture freely.
The damage die would be a d4 (RAW)
The spell has you throw the weapon, so you are not holding it all. You are definitely not holding it with two hands and ready to use it as required for the extra damage. Staves not held by two hands have a d4 damage die. (Explained in detail below.)
The damage die would be a d8 (RAI)
Paizo themselves have ignored the rules ...
Take Druid Dedication, you can retrain it later
The scaling of Occult or Divine spellcasting is important only when it improves over trained. That happens with Monk Expertise on level 9, so you have plenty of time to take a General feat (Adopted Ancestry) and an Ancestry feat (Adapted Cantrip) with any race.
I would retrain Druid to Cleric dedication just ...
At this time there is no method
Unfortunately, there isn't a way to do this. The spell components are simply the spell components and there currently no way to add a component that isn't listed.
I had a similar issue with the Bardic Instruments and their ability to only work on spells that Charm to force disadvantage. There just weren't/aren't a lot that ...
Your instinct is correct: the artificer is more like a cleric than a wizard when it comes to spells known. They prepare spells daily from the complete list available (which includes subclass spells).
The mechanism for changing the spells prepared is at the bottom of page 11 of TCOE:
You can change your list of prepared spells when you ...
Electric Arc as an innate (Charisma) Occult or Divine spell
Virga May (Storm Hag) Changelings (a versatile heritage, although somewhat lore-locked) can start with Electric Arc as an occult cantrip.
Wellspring Gnome with First World Magic can start with a primal cantrip but casts it as an innate arcane, occult, or divine (chosen at character creation). Bonus, ...
You can make your concept with an Archaic Wayfinder and a friend that can cast Electric Arc. This would allow your Monk to cast it once per combat* fairly easily until you are able to pick it up yourself, and Archaic Wayfinder is available at level 2 and you should have access to it in PFS (although I'm not actually familiar with the PFS rules, AoN ...