Singapore has representatives of many major religions.
Islam
There is an organization devoted to Muslims - MUIS http://www.muis.gov.sg/cms/index.aspx
A related list of mosques can be found here http://www.muis.gov.sg/cms/services/MosqueLSummaryDL.aspx
Below are some well-known & accessible mosques & their addresses:
Prayer times can be found at this website http://www.muis.gov.sg/cms/view.aspx?id=526
The prayer times for 2010 can be downloaded here - http://www.muis.gov.sg/cms/uploadedFiles/MuisGovSG/Downloads/Prayer%20Timetable%202010.pdf
For halal food please see the halal food section
There are also many Buddhists, Christians and Hindus in Singapore.
Hinduism
Around 5% of adult Singapore population follow Hinduism. Their needs are met by 24 well-established temples in the city. Here is the complete temple list of Singapore http://singaporehindutemples.com/templelist.html. Two government bodies deal with all Hindu affairs — The Hindu Endowments Board and The Hindu Advisory Board.
Christianity
Christians in Singapore constitute 18% of the country's total population. The majority of Christian churches are under the umbrella of the National Council of Churches of Singapore.
Click this link to see a list of Catholic churches http://www.thecatholicdirectory.com/directory.cfm?fuseaction=search_directory&country=SG&absolutecity=Singapore. Click this link to see a list of methodist Churches: http://www.methodist.org.sg/contact-us/find-a-methodist-church-all.
Buddhism