I’m a Disney vet, but never have gone with a toddler before. Our son will be under 3 when we go, which means (please correct me if I’m wrong):
For all intents and purposes, bringing an infant into the park is like bringing a purse into the park, at least from an an entry gate perspective? 
I’ve Googled this but no one’s language is as definitive as I’d like.
Correct. Only guests 3+ need a ticket. Children under 3 can still ride anything they are tall enough for and experience anything they are capable of experiencing. They don’t need Genie+ or ILL, even if they take up a seat.
You should still include them as a person on ADRs. They will generally not be billed for food at prix fixe restaurants, but they will typically be given some food (usually a kid’s meal type of situation) for free.
Again, correct. No admission or documentation of any kind are required. I have never been questioned about the age of the my children, although once I was asked if my child who DID have a ticket was really 3 and hinted at that maybe I didn’t need to have paid for their ticket (my kids are petite). That all said, you may want to bookmark their birth certificate on your phone somewhere so you can prove they are under 3 just in case you get a very difficult CM.
Not a bad idea - our son is rather big for his age, but fortunately somehow still ‘reads’ baby… like every single little girl at every playground we take him to, even though he’s twice their size, will go ‘Hi baby!’ It’s crazy.
That’s a great age to go. Have all the fun.
Yes, except …
Your purse doesn’t go potty at the least opportune times, cry when meeting certain characters, or bail on rides at the last minute after waiting in line.
That said … I loved being at Disney with my son when he was 2 years old. Hope you have an amazing time!
Also, plan to be very flexible and to bail on anything at any moment if necessary. Most of my day at HS was spent watching my almost two year old push his own stroller. And we left early so he could have a proper nap and I don’t think we returned that night. I loved that trip and it was a very different pace than our past trips. There is very little at HS for kids under 3. More at the other parks.