Regarding the stroller on bus issue, for a mum on her own, at times its difficult cos you have to make sure the stroller fits on the way up the bus.. some buses have a bar in the middle at the entrance, generally speaking the stoller should fit, not unless its those double stroller (like for 2 babies)types. As for a place to store the stroller, some buses now have standing room area or a particular seat that has some space right next to it, likewise as what was said, it really depends on what time of the day you are travelling and how lucky you are to get that particular spot/ seat. To share an experience, (not that i think you your wife is going to do the same) i once encounterd a couple who placed the stroller plus kid at the standing area, while they sat at the seat right next to the standing area, the bus made a turn, the stroller n kid went hurling down the steps n i stopped the stoller in time before the kid went flying down the steps.. this despite the stroller having been "locked".
Now for the wonderful "flagging a taxi" issue.. i believe it has become a little better somewhat after cab fares went up. I noticed many foreigners/ expats sometimes flag for cabs at the "wrong" places. It would prob take a while to learn where you should or should not flag cabs. Places with zig zag yellow lines on the road (some or most cabs would not stop cos they might get fined) or the wrong side of the road!! i have seen many a tourist/ expat try to flag for a cab on the right side of the road which is the fastest moving lane.
Regarding the odd thing about singaporeans liking to Q, its simply cos the taxi companies are trying to prevent touting or unfair practices such as taxi drivers cutting each other off/ fighting for fares, so the drivers are REQUIRED to pick up passengers from a taxi stand if there is one within that few metres (if you get what i mean) and passengers are REQUIRED to q-up at a taxi-stand to prevent them from walking a few yards in front of someone who has been waiting for a while. All these apply to areas where there are taxi-stands, usually in town/ business district/ malls/ clubs etc.. in housing areas, there arent any so at certain times of the day where demand is high, taxis are scare, you get that situation of someone walking a few yards ahead of you to get a taxi first..
of course, it is not impossible for one to "turn a corner" and flag a cab while a long line of people continue to wait stupidly in the q.. sometimes its due to the driver not wishing to drive into a particular area, cos its jammed or the person has walked far enough away from the taxi stand.
last bit of advice would be, as someone new to town, you would learn where are the places/ streets that would be easier or more probable for you to flag a taxi. It could be as simple as crossing the street or walking to a particular area. I have never been able to get a taxi when i walk to the main road right next to my place, but if i go to the back, where the little roads are in the housing area, i always get one, plus the coffeeshop is where all the drivers take their break!
Hope all these help!