Dear Vinodha
Welcome to IL and to Singapore and may your stay be pleasant in both!
1. Yes it is the correct procedure to go thru agents to rent a condo apartment or HDB apartment in Singapore.
2. Please lookout for maid agencies(TRUST certified) in straits Times Classifieds and tell them your requirement. They will help you to find a suitable one. You can interview the maids personally and choose. Alternatively, Katong area has many maid agencies, you can directly drop there to choose one as they have a lot of maids available for interview. From my experience Indonesian maids with working experience in Singapore are better than others and they handle kids well and also learn Indian cooking faster.
Best of Luck.
Cheers
Vijee