I have been dating a guy for two months, and he invited me to his apartment for the first time a few days ago. I was shocked to see the way he lived because his home was a mess. There were unwashed dishes in the sink, clothes strewn carelessly on the floor, and it looked as if nothing had been cleaned for months. This was a shock because he is clean, appears to be well-organised, and has never given me the impression that he isn’t serious about personal hygiene. I am now rethinking everything since I saw his place because it feels as if he is just putting on a façade while going on dates with me. Should I end this relationship if I can’t be with someone who doesn’t know how to keep a home clean?
Did you consider telling him how you feel and asking him about this? It’s perfectly okay to not date someone who doesn’t take hygiene seriously, but it’s also possible that there may be an explanation that isn’t being considered. This isn’t to justify the way he lives, but it’s always better to make any decision after you have considered all the facts, before assuming that someone is pretending to be who they are not. Tell him why it’s unacceptable and ask him to clean his place up. Having said that, if your feelings for him don’t run deep enough, this is as good a reason as any for you to stop dating him.

Is it possible for two people who work together and have been in a relationship to continue being friendly if things haven’t worked out? 
That depends entirely upon the people in that relationship, the discussions they have had about drawing lines between personal and professional spaces, and how badly they want to keep things normal in an office setting. It isn’t impossible, provided both partners have a clear understanding of why things are the way they are, and what they need to do to avoid unnecessary awkwardness.