By the way, if I'm not mistaken sometimes the honorific form could be "ご + masu stem + になる" depending upon the following kanji though both are 御 in kanji which is usually not used in this context, aren't they?
Right. Kanji 御 can be used with on'yomi verbal nouns, but it's rarely used. 御 is almost never used with -masu stems.
By the way, some na-adjectives and most verbal nouns take the prefix ご instead of お to become honorifics. Does the honorific form "お + masu stem + になる" ever take ご instead of お for some verbs?
As for お vs. ご, yes, it's the same as "お + -masu stem of verb + ください" / "ご + Chinese origin (= on'yomi) verbal noun + ください" in the following thread.
~て下さい is usually used as a request to someone for doing a favour. Sometimes we respond to a request by saying ...~て下さい which means feel free to do it. I suppose it all depends upon the context again. Without any context, I would interpret the sentence below as a request. Somehow this sentence...
jref.com
You need to notice that ~になる has another meaning "to become ~". Adjectives express a state, not an action, so ご立派になる, おきれいになる and お静かになる are just polite forms of 立派になる "to become excellent", きれいになる "to become beautiful" and 静かになる "to become quiet/calm", respectively. Thus, "お/ご + na-adjective + になる" is not an honorific form.
Also note that "お/ご ~ になる" can't be used for all verbal nouns (e.g. ×ご運転になる, ×ご行動になる). Other honorific forms "~なさる" or "~される" are more commonly used for verbal nouns.
Then I presume the honorific form "お + masu stem + になる" would be applicable only to most godan verbs or where alternatives are not available.
I meant "ichidan verbs whose -masu stem is a single kana or irregular verbs whose -masu stem is a single kana" by "ichidan verbs or irregular verbs whose -masu stem is a single kana" in my previous post. I should have used another word order "irregular verbs or ichidan verbs whose -masu stem is a single kana" since irregular verbs are just only two, as jt_-san mentioned, and the -masu stems of them are both a single kana.
Anyway, "お + masu stem + になる" can be used with other ichidan verbs than 見る, 着る, 似る, 寝る, 得る, 煮る or 射る (e.g. お止めになる, お受けになる, お掛けになる). Sorry if my exlanation was confusing.