The reason that you being off sick didn't come up in conversation is that an interviewer is highly unlikely to ask "Are you off sick at the moment?". There are, however, likely to be questions such as "Tell me a bit about your current role and responsibilities", "Talk me through your last 20 years at Company X" or "What is it that's made you look for another role" - all of which would have been your cue to explain your present circumstances.
You haven't lied, but you also haven't been transparent, and that may well come back to bite you now.
With regards to your notice period, you should have known what your notice period is when you interviewed for another role, were you not asked? Maybe it never came up in conversation...
It's a critical piece of information for any employer as everything hangs off the date that you are expected to start, so I'm surprised it's being discussed post offer.
I have made an offer to a candidate who couldn't confirm their notice period - contractually it was 3 months, but the candidate was hoping he could negotiate that down to 1 month.
As an employer, I understood this and allowed him a week post-acceptance to try and negotiate this before confirming a start date.
He asked, they said no, we had to wait the 3 months.
The difference here is that he was totally transparent pre-offer, so we could make an informed business decision as to how we proceeded.
It doesn't sound like that is the case with your situation.
I know this might sound negative, but if I was your new employer and these things started coming out I would have alarm bells ringing all over the place right now.
Assuming they still want you as the facts emerge, I'd be surprised if they don't put you on a fairly strict probation plan and watch you like a hawk...
You haven't lied, but you also haven't been transparent, and that may well come back to bite you now.
With regards to your notice period, you should have known what your notice period is when you interviewed for another role, were you not asked? Maybe it never came up in conversation...
It's a critical piece of information for any employer as everything hangs off the date that you are expected to start, so I'm surprised it's being discussed post offer.
I have made an offer to a candidate who couldn't confirm their notice period - contractually it was 3 months, but the candidate was hoping he could negotiate that down to 1 month.
As an employer, I understood this and allowed him a week post-acceptance to try and negotiate this before confirming a start date.
He asked, they said no, we had to wait the 3 months.
The difference here is that he was totally transparent pre-offer, so we could make an informed business decision as to how we proceeded.
It doesn't sound like that is the case with your situation.
I know this might sound negative, but if I was your new employer and these things started coming out I would have alarm bells ringing all over the place right now.
Assuming they still want you as the facts emerge, I'd be surprised if they don't put you on a fairly strict probation plan and watch you like a hawk...