You taste along the process to understand and experience what your wine is going thru. Then if at any point in time you run across something askew you may be able to cure it before it becomes gallons of drain cleaner.
Fortunately I've not experienced that but it does happen.
this is exactly right. eventually, you can "see past" the flavor at that point and see where the wine is headed. i've had my mother taste the wine sometimes and she's always, "this is awful!" Six months later and she's like wow, this is so much better. I'm thinking, why, i haven't modified it at all, besides maybe back sweetening.
wine will taste a little yeasty, dry (depending on how far it's along) and slightly more acidic/bitter. Depending on type and what level of acid is in it. Back sweetening and aging will help reduce the bitterness and dryness. The fizzy taste will go, if you give it a splash racking. Rack it by just pouring it into another carboy (no siphon) before you go to bottle it. the flavor should be better with a little back sweetening too. i'm not familiar with kits, so i cannot tell you how "full" bodied that wine will turn out. i recommend either searching, starting a new thread or pm'ing someone here to what brands/kits work best for your goals.