Symptom #1:
The last couple times I've taken my skiff out I noticed the motor would hesitate for a second after giving it throttle when taking off to get the boat on plane.
It seems like the motor takes a second to recognize the throttle position and then it kicks in. A little unnerving sometimes because there is a little delay and then the boat accelerates all of a sudden.
It doesn't seem to do it every time but a good majority. I've tried varying acceleration and I believe the issue remains except for maybe really slow acceleration.

Symptom #2:
This only happened on the last trip. I was powerloading the boat onto the trailer. Was using minimal acceleration to get on the trailer and line everything up and then increased throttle to push the boat up the bunks. When increasing the throttle the motor shut-off and I never made it up the bunks. I retried several more times and same thing happened. Finally made it up the trailer by only getting a little more of a head start and didn't have to give it the little extra gas. On one of those attempts it took me a couple cranks to get the motor restarted.

All else runs and operates great from what I can tell. I've put fresh fuel in almost every trip and use fuel stabilizer with every fill up.

My suspicion and plan:
I bought this boat in 2010 and the previous owner has taken real good care of it. I have not replaced the fuel/water separation filter since then so I plan to try that first. And maybe look at the inline fuel filter (I suspect it has one under the cowl). My first guess is a fuel issue.?
I'm not completely mechanically ignorant but I've never troubleshooted outboard issues. Any other suggestions for troubleshooting?

Thanks in advance for your help.