Yes yes, ‚please to meet you‘ is a very common mistake that non-English people make. Just remember the whole sentence and it makes a lot more sense „I AM pleased to meet you“. You wouldn't say „I am please“ now, would you?
Also, „how do you do“ is vistually extinct. Maybe the queen might use it on a good day, but the „How do you do?“ „How do you do?“ greeting exchange has now been replaced by „Alright?“ (which you also don't reply to, just say „Alright?“ back, just like with „How do you do?“). The whole sentence is „Are you alright?“, but the sound you usually get from people is a quick „Aight?“. Oh, the English and their love for abbreviations, lol.