How Do You Win Lane Against Singed?

Like I said, expect dives. Always ward your top jungle because he will most likely farm behind your own tower and also champions like vi will usually come from behind and just press r. Since singed players will usually just try to get the tower focus on getting objectives on other parts of the map since kayle ult is good for teamfights. The thing I have learned from good and bad kayle players is that usually the bad ones will stay top the entire game and use their ult for only themselves and good ones will move around the map with the team and ult to save team members from trading kills.

Oftentimes, yes.

You mentioned that Vi had to ult in to kill you under tower; that means that 1) she's an idiot for ganking an unpressured Singed lane, and 2) she's not providing pressure elsewhere. Your jungler can counter-gank, as long as he/she doesn't chase Singed, but would be just as well off or better trying to get someone else fed. Again, Singed is annoying and hard to kill, but he's going to have a hard time in team fights even if he's fed. He's a pest, not a game-winner.

The ultimate counter to Singed is just winning the game at hand, because if you're not playing his game of cat-and-mouse and he's forced to dive with a jungler for kills, he's a burden for his team.

Yes, he's painful to play against and probably the most anti-fun thing since lag. You just have to rely on your team doing their jobs, and then treat Singed like a whiny kid: don't appease him, just go about and do the grown-up stuff that lets you win the game.

Edit: And for the people down-voting the OP, it's an honest, if frustrated, question that a lot of people have had in the past. Stop it.