Did English peal derive from pea by analogy with kneel and knee?

No. Different linguistic root entirely. English vocabulary is not really subject to rational analysis — the words are derived from so many different tongues, the spellings have changed over the years, and many of the meanings have been altered as well. Check out an online dictionary of Indo-European roots.

No. No relation at all.

Pea was originally called pease. People assumed that was the plural and "pea" was the singular.