Sometimes yes, it mostly happens on the fleet fight screen. I don't really buy the idea that the 1.0 version didn't have this issue, it's just that given that it's not very used, you won't notice it much... Back in the day there were less laggy situations as you'd use the game only on lans, who knows what happens now beneath the hood.

My observations are: crashes happen either on fight start - even when you click on auto-calc - or, more rarely, on fight end. Any other case that I've witnessed was due to some internet issue. Crashes may happen once every 100 battltes or so, and I have the feeling that a possible reason is that one of the two players has clicked on tactical fight while the other has clicked on auto-calc, but that could be wrong and/or not the only reason.

Some other time there's something that goes wrong inside the game and it gives me a "can't draw pixel" or similar problem, I'll write it down the next time it happens, Praetor manages to continue when that happens but I've not managed (I'm on win 7 he's on 10) - I simply get over and over again the same popup.

Basically it's something you can live with, just keep saving often, and if it happens the two players normally re-play in the same way to avoid having an external event - the crash - influence the game. So, no moving ships or heroes away, no preventive scrapping, and in general no acting based on the knowledge of what's to come. Obviously that becomes harder the more time passes after the last save, so save often... I get Praetor mad cos I keep forgetting about it :P
PS on the schedule thing, nobody can keep one ;) we just meet on gameranger, have some contacts on hangouts or wazzup, and if we get lucky we have a fight or continue an old one.
Due to the few slots, generally you archive the older fights - I zip them in a file with the name of the other player for example. It's simpler than it might sound.