SQ flights from SIN to MAN used to be non-stop but they started a stopover in MUC earlier this year. I have no idea how many pax from SIN continue to MAN but I don't expect many pax joining the flight in MUC.

How many immigration lanes are open for non-EU pax varies accoridng to demand to some extent at least in T1. Last week I arrived in T1 shortly after the EK A380 fromDXB and there were hundreds of people, mostly students arriving/returning for the new academic session from Asia, in the non-EU queue for immigration. At least 4 non-EU lanes were open but it probably took at least an hour if you got stuck behind the queue.

MAN T2 is not just a charter terminal and morning arrivals include QR from DOH, VS from MCO, CO from EWR before SQ (at this time of year anyway - maybe different in December), and a couple of TATL arrivals after the SQ flight.