Of course it is never somebody's fault for their partner cheating. Basically, if there is a problem in the relationship, either talk about it to them to make it better or end the relationship - don't go looking for comfort elsewhere.
But for all that, Dan and Nicola has been building for quite some time as neither have felt able to properly talk to their other halves, have felt neglected, misunderstood or unwanted (for different reasons) and they have a bond die to Dan having helped get Nicola out of the fire. A close friendship has developed, it momentarily crossed a line which they both deep down knew was wrong and regretted. Very different to full on cheating.
I don't really see how the Nicola situation impacts on his ability to be a very good Carer. That's personal, his job would be professional. Yes he might develop an affection for some of his charges (that would probably be his biggest problem, getting too fond of them so being very upset when they die) but not in the way he has with Nicola where he did save her life and they knew each other beforehand anyway.
My Mother did have Carers in her final weeks and i'd have had no issue at all with somebody like Dan turning up. Kerry i might have simply because of her Tyne tunnel gob - she's very likely t make a 'joke' which is quite upsetting or offensive without meaning to.
As I said in my first post, Dan is kind, gentle, patient, practical - ideal attributes for a Carer.