Sure, in that universe. It seems evident that every version of Spidey gets that message at some point (it's what Across the Spider-Verse calls a "canon event"). The Tobey version got it from his Uncle Ben.
Agreed. The initial implication was that he might have already gotten it, in his backstory, but they didn't make it explicit. When No Way Home gave connected MCU Spidey back to more classic Spidey themes and content, they gave the line to Aunt May to put it on-screen, and it would be weird for him to have received the speech twice.