What exactly does "Safe to leave" mean?
A game becomes safe to leave when someone abandons it (abandon means that the player was disconnected or away from keyboard for 5 minutes, or just pressed Leave Game).
If you disconnect from a game, which is safe to leave or will become safe to leave before you abandon it, you don't get an abandoned point. However, you will still get a win or loss point, depending on how the game ends. Usually this will be a loss, because your team will be much weaker without some players.
If all 5 members of a team abandon the game, they automatically lose in a few seconds.
If someone disconnects from a game and doesn't reconnect before first blood, or simply abandons it before first blood, the game will be safe to leave and no stats will be recorded, which means that nobody will get a win or loss point or battle points.
A game will be recorded in your game history even if it's safe to leave and no stats will be recorded, but don't let that confuse you: that doesn't imply you get points for it.
Now I will answer your exact questions and show some more examples.
If you leave the "Safe to leave" game and start another, will it count as loss?
If "no stats will be recorded", nothing will count.
If it's just safe to leave, it will count as a win or loss depending on whether your team won or lost.
If you continue playing the "Safe to leave" game and you win, will that win count?
If "no stats will be recorded", nothing will count.
Otherwise, a game being safe to leave changes nothing in this aspect, and the win will count.
If the game gets marked as "Safe to leave" does that means someone from enemy team can leave the game too and not get any loss or abandon point?
When a game is safe to leave, anyone can abandon and not get an abandoned point, but they will get a loss or win unless "no stats will be recorded".
If you leave a game and your remaining team members win, you get a win unless "no stats will be recorded".
If someone disconnects from a game that is not yet safe to leave, then you disconnect, you will not get an abandoned point, UNLESS they reconnect before their 5 minutes run out. (Not entirely sure about this one.)
If someone disconnects from a game that is not yet safe to leave, then you disconnect, then they reconnect and you don't reconnect before your 5 minutes run out, you will be the first one to abandon the game and will get an abandoned point.