Hello there!
"Es geht" is very common in German. It's mostly used as a synonym to "funktionieren". "Es geht" -> it works; "Es geht nicht" -> it doesn't work.
And because every German thinks everything may work or not, you can apply this to a lot of things...
Q: "Kannst du das übersetzen?" (Can you translate that?)
A: "Geht nicht" (It doesn't work / No, I can't translate that)
Q: "Gibst du mir das Werkzeug?" (Would you give me those tools?)
A: "Es geht nicht" (It doesn't work / No, I can't ['cause they are stuck])
Q: "Bitte gib mir ihre Telefonnumer!" (Please tell me her phone number)
A: "Geht nicht!" (It doesn't work / No, I can't ['cause I'm not allowed to])
We Germans even make fun about that, like:
Q: "Was geht?" (What's up?)
A: "Alles was Beine hat" (Everything with legs)
And yeah... it's a really lame joke. ;)
Remember, it could also be used as an expression about your mood or health...
Q: "Geht es dir gut?" (How are you?)
A: "Es geht" (So-so / Not too bad)
"Es gibt" on the other hand is rather specific and can be translated with "there is".
"Es gibt keine Bratwurst mehr" (There is no Bratwurst left) (You knew I'd take such an example, right?)
"Was gibt's (denn)?" therefore means "What is it?" or "What's up?" (e.g. as a response to beeing called over by someone)
Unfortunately is "Heute gibt es keine Zeit (dafür)" no real sentence in German, although everyone will understand what is meant - it's like "there is no time today", as if time doesn't exist...
You'd better say: "Heute ist keine Zeit (dafür)" or "Ich habe heute keine Zeit". But that depends on the context.
Hope this helps.