I read some similar questions (e.g. this), but they concern European airlines that have to act under European laws, Singapore Airlines probably doesn't.
I booked a flight from FRA to SIN (and further on, 4 legs in total back and forth). For all flights but the one mentioned, there were enough seats to select online one that wouldn't cost me any extra money. For the FRA - SIN flight there were only seats left they would charge me extra.
Obviously I don't have to select a seat now before checking in prior to my flight.
a) Will I have to when checking in online?
b) If not, will I probably just get any seat that is unoccupied at the time of checking in at the counter?