If time runs out and the PM, whoever it then is, decided on Remain to avoid a cliff edge, then I would be astonished if the E27 imposed conditions like the Euro.
They would much prefer we stayed, because although the damage to the E27 would be much less than to the UK, it is not negligible either.
So, any negotiator, even DD, should be able to ensure we even keep our current opt-outs, i.e. Remain would just be status quo
The only condition the E27 might insist on, is that Remain must be for a minimum period, probably at least 10 years - some at Brussels are concerned that otherwise the UK might mess about calling and revoking A50 repeatedly, to try to get a better deal.
If the UK actually Brexits in March 2019 and then applies to rejoin the EU, that would be totally different:
it would be a new application, with all previous optouts wiped out
However, even then, the UK economy is unlikely to satisfy conditions for us to join the Euro - e.g. annual deficit too high - so joining the Euro would be postponed.
Anyway, it now seems that new members can choose to join the Euro when they think the time is right, which may be never !