"Vous savez ?"
In spoken French, questions are almost always indicated just by tone of voice. Inversion (Savez-vous?) is mainly used in writing. In English, both forms are acceptable--You know? and Do you know?--but they have slightly different meanings, as you've pointed out. In French, there is no difference in meaning, only a difference in how informally they come across (you would not use Vous savez? in formal writing). Hope that makes sense!
From what I understand, connaître means to be familiar with. For example, we would say "I know this street," or "I know him, we met at school."
Savoir is more to know as a fact. As in "I know that you're angry" or "I know the answer is five." It can also be used in the sense you mentioned, adding a "how." So "Do you know how to drive?" would be "Savez-vous conduire?"
Someone please correct me if I am wrong.
Hey, Sitesurf, I have noticed non-French natives on social media write "j'suis... (whatever)" and just assumed they mistakenly dropped the "e" in je because they heard it said that way.
Now, I see you wrote "t'sais" which makes me think it is not unusual to drop the vowels that way, albeit informally, to sort of mimic how the phrases sound. Is that correct? A kind of shorthand way of writing among friends, not unlike how I may text my friend "Hey, JJ, 'sup?" when I really mean, "Hey, JJ, what's up?"
Is that the case?
Yes, that is right. "je" and "tu" are often "elided" in speech: "je suis" becomes "j'suis" and the sound of it is "shui".
Some words disappear, "ne" in negations, for example: "je ne sais pas" becomes "j'sais pas" (sound "shais pas").
You may find those in writing in novels or theater dialogues when the author wants to convey the way characters are supposed to speak.
But in the media, quotes are generally "rewritten" to look right.
Your proposal is grammatically correct, but it is not only a translation but an adaptation. We don't know, from "vous savez ?" what is known, since there is no context. You could invent many other variants, but none of either would simply translate "vous savez ?".
- do you know how to? = savez-vous/sais-tu comment faire ?
I find looking the word up in a dictionary like Larousse can often help you understand a suggested synonym that you find confusing.
In this case, I believe savoir is given the synonym "can" because when you "know how to (do something)", it can be said that "you can (do that thing)".
je sais lire
= I know how to read => I can read
"connaître" is used with people and places and "savoir" with facts and things learnt:
Therefore, you know = tu connais, vous connaissez OR tu sais, vous savez
you know France and French people = tu connais/vous connaissez la France et les Français
you know your lesson = tu sais ta leçon/vous savez votre leçon