Are they a problem in Singapore?
I’ve never been bothered by mosquitos on all my visits to Singapore over many years. Maybe if you are walking/hiking in Nature Reserves it would be an issue, so bring insect repellant if you are choosing outdoor/nature activities.
No issues. If you're worried, you can purchase repellent from any of the local pharmacies or super markets.
The Singaporean authoriries encourages people to regularly check locations around their properties to find any areas of standing water that might be used by mosquitoes for breeding. By doing this, it really minimises the amounts of mosquitoes in the urban areas. I don't recall being bitten even once in the city. Not even in the botanic gardens
As mentioned, in nature areas (including the zoos) it is a good idea to use some repellant if you are a bit of a mosquito magnet.
Not that big of a problem that you'd need to be concerned about, in my opinion. Do put on some mosquito repellent if you want to avoid getting bitten at all costs, especially if you're going to more forested areas like Singapore Zoo, Bukit Timah Nature Reserve, Sungei Buloh, etc. However, it's not a problem that I spend too many hours thinking about in my day-to-day life here :)
Not such a big problem. Singapore is very alert to mosquitoes and mosquito borne diseases. Our geographical location and climate is such that it is impossible to get rid of mosquitoes, however, the National Environmental Agency is very proactive about measures to control mosquito breeding. Mosquito borne diseases usually appear only in certain pockets mainly in the residential areas and construction sites. By and large, mosquitoes are kept under control in most of Singapore. From a tourist perspective, the risk of being exposed to mosquitoes and mosquito borne diseases is not great. For safety, you can use an insect repellent/ patches when walking in the nature reserve areas or grassed areas.