Zoo with Daughter: Birds: C&C Requested

[jedirunner]

Wanted to make a second post to get some comments on how to get sharper bird photos. I've been watching the amazing bird shots here in the forum, and hoped for some comments and suggestions.

These are at high ISO (either indoors or outside in highly overcast). I feel somewhat dumb for not using a flash. I also feel bad that at bird identification I am about 17 levels *below* noob. I'll have to start learning there as well. Anyway, these pics were brought into iPad as RAW files, and cropped in PhotoGene. Almost no other processing than cropping (might have tweaked a setting somewhere on one of them, but I don't believe so).

Questions:

1. Would you use flash on an overcast day? Or would you bother with bird shots at such high ISO?
2. Should I be backing off the zoom to try for sharper focus?
3. I feel like in some of them I might have been sharper at a narrower aperture, but then I'd have to decrease shutter speed or increase ISO even further ... I don't want higher ISO really, but might have been safer at slightly slower shutter speed?

1. 300mm, f/6.3, 1/500, ISO 1250


2. 300mm, f/5.6, 1/500, ISO 5000


3. 300mm, f/5.6, 1/500, ISO 12800


4. 300mm, f/5.6, 1/500, ISO 6400


Thanks for any comments and suggestions you have for me!

Kevin