It also kicks into incest mode once the first arc is over with, so yeah maybe just watch that.
It definitely hints, but I wouldn't say that it goes really any farther than that (and even that doesn't last long). The fact that there is an outright canon love interest by the end of the first arc sorta relegates any other relationship teases to the "if you ever leave this person then I'm going for them" realm (which certainly happens enough in the real world).
As for Log Horizon, I never really got into it just because it seemed like they hadn't fully accounted for just what the inability to die would do. Like with the bandit guy they end up playing his defeat up like it's this huge thing when it happens (if they changed later I apologize, I didn't get too far beyond this) when in reality all they did was slightly inconvenienced him with a level penalty (even less so if players give xp, which would mean he would just have to sit outside and farm players for an hour or so). The fact that the only way to beat a large group of people at their own city would be to somehow imprison them with no way for them to get killed or kill themselves (else they would just keep perma-respawning at the cathedral, meaning you'd be facing a loss by 1000 cuts from them, while your people spawned back at your cathedral several days away) didn't seem like it was really being considered.
It looks like you didn't watch far enough, or you're making huge assumptions about what happens at the end of that arc (episode 5).
Most of those points miss the mark completely.
Their goal wasn't to kill him in the first place or permanently defeat the enemies, it was a rescue, which succeeded, so they couldn't give a shit whether he perma-died or not, as long as he got out of the way long enough for them to escape. So, killing him was never a plot point, he was just in the way and needed to be not in the way. Inconvenience someone for 1 hour is plenty when all you want to do is rescue 1 person. They temporarily confuse the enemies and get the hell out of there, because the show HAS fully considered the fact that the enemy cannot be killed. Those guys remain in charge of their fascist little city as the show goes on ...
I recommend keep watching Log Horizon, because it's not really about battles at all, the first battle was just to fill the viewer in a little about how the game mechanics works.