Yes

Yes , you can take pictures from outside . Try going on a full moon night to get a spectacular view of the mosque .

I doubt that the Sultan Mosque would be closed to infidels during Ramadan. I’ll be in the Middle East this Ramadan, and expect no problems in either Egypt or Istanbul. Southeast Asian mosques in general are much more welcoming than those in the Near East (let alone those in North Africa anywhere between Cairo and Morocco). Time your visit though: avoid going during prayer times, and go when it’s sunny (to get the best photos of the dome). I’d avoid going on a Friday during Ramadan. Checking with your hotel might be a good idea. Obviously being covered from neck to wrists and ankles is important any time of year. I discuss masjid etiquette, as well as the Sultan Mosque’s architecture and history, at some length in my TA review of it. Three points of etiquette I did not put into my review are (a) always step into the mosque with your right foot first, and exit with your left foot first; (b) if sitting, keep your feet pointing away from the mihrab, just as in Buddhist temples you never point them at the Buddha; (c) during Ramadan, don’t display, let alone consume, any food or beverage in the vicinity of the Sultan Mosque. Since Singapore’s primarily non-Muslim, eating and drinking anywhere else in town is no problem. If you’re planning to see the Southern Ridges, Bukit Timah, Buddha Tooth Temple, National Museum, or Singapore Zoo, you might my reviews of those attractions useful. Pity Singapore’s so expensive: it’s my favourite city in the world.

Yes, women are allowed. Shoulders and legs have to be covered, but in case they aren’t, they provide you with specific clothes you wear before entering

Yes, women are welcomed. Might have to add a provided shawl depending on dress.

No si paga niente! Ma si deve essere cortese e viene vestito correttamente. Si lascia, naturalmente, scarpe furori.

Hi. No form was needed and no fee was charged when I was there. I just arrived and a very helpful 'worshipper' explained many things and answered questions for me. Language was a slight barrier. Enjoy!

From what I've seen, there are no 'tours' in any of the houses of worship in Singapore. If the mosque is open; they aren't in the middle of prayers, then you can take off shoes and socks and go in. These are religious establishments, not museums. If you're quiet, polite, decorously dressed, however, you'll be welcomed... just look closely before taking a photo. In some houses of worship there will be discrete signs reading; No Photo or No Entry. If you follow their requests they'll be delighted! Remember to have $1 or $2 in a convenient pocket of a donations or charity box. And yes, Zam Zam is an excellent idea before / after your visit. If you sit at a table on the footpath of ZamZam, you can enjoy the view of the back of the Sultan Mosque while eating their delicious food!

yes, there is a dressing code where you have to cover yourself with provided attire. worry not.