Orim's Chant, Silence, and Abeyance do not affect spells played before them. They only stop the player from playing any more spells after they resolve. So your opponent can respond to Silence by playing a Lightning Bolt, for example.
Also, we don't use the term "fizzle" anymore. Just countered.
1: My opponent cast a spell, I respond with Silence. Will his spell go off or fizzle?
Their spell will still resolve.
2: My opponent cast a spell, I respond with Orim's Chant. Will his spell go off or fizzle?
Their spell will still resolve.
3: Are Isochron Scepter + Silence/ Orim’s Chant combo really legal in Legacy? To me this combo seems more lame than Trix or Memory Jar.
Yep. Check out the Legacy banned list
here.
4: Is the Dark Depths/ Vampire Hexmage combo legal in Legacy? I mean… they ban Tinker for being able to get a turn 2 Colossus. But if a turn 2 (using maybe Dark Ritual) 20/20 indestructible creature aint even more lame, I don’t know what else to say… and why is it people are so fond of Tarmogoyf and Baneslayer if they can get a turn 2 Marit Lage?
Yep. Check out the Legacy banned list
here.