Note 3 - great phone - if you can palm a basketball. (Remember one of the criteria - easy one-handed operation.)
Synchronization with Outlook calendar and contacts doesn't depend on the phone, it depends on using the right apps and setting them up correctly. There are lot of articles on the web about how to do that. (And there's more than one way of doing it.)
Battery life. Let's face it, guys - a given iPhone has better battery life than the equivalent Android phone. Android is inherently not great on battery life. Some Android phones are battery pigs, others can go 4 days with light use, but for a phone that can be on for 8 hours of heavy use without charging, most Android phones would require 2 batteries and a swap before the day is out. (Unless you want to have 2 extended batteries, a large case and have one battery charging at home while you use the other one. 8 hours of screen time? Not on most smaller Androids.
Lambrosio, I don't think you're going to get what you're looking for. I love my Note 3s. I carry a pretty powerful computer in my pocket, the screen is large enough for 71 year old eyes, and I know how to get the maximum life out of my batteries (I still use an 11 year old phone with the original 2 batteries - I always buy a spare battery for a phone). But I'm not on the phone all day. I don't send 30 texts per hour. Some days the phone sits in my pocket all day, never being used. But 8 hours of phone calls? I think you'd need a spare battery.
As far as recommendations, a Samsung S4 may be small enough to be comfortable for you. Or even an S4 mini. (How young and how good are your eyes?) They're good phones, and with a spare battery, either one should last you all day. (Get a spare battery with a charger that charges the battery out of the phone, so you can charge both batteries at night.)
But it's still like ice cream - what's a good flavor? There's a lot of personal choice in a phone. (I won't buy one with a non-replaceable battery or without an external SD card.)