Is the font in logo 'B' too thin or small (for the word Education)?
no
Does the red outline in logo 'A' make reading it harder on the eyes?
Yes. Saturated blue and saturated red do not work well together. They can cause a lot of eye strain. This will also be harder to print.
Does the brighter blue of 'logo A' make it more eye-catching?
No. It makes it more jarring and harder on the eyes.
Logo 'A' has an accurate ECG rhythm, while 'B' is stylized, but inaccurate. Does this accuracy matter in regard to logo creation?
No. Logos arearen't literal.
The ECG line in 'B' is centered. Is this balance generally considered more effective in logo design/branding?
There's no rule here. You do what works for the particular logo you are working on.