I've never been at night, but I would assume it is just as safe as anywhere else in Singapore, which is to say that it's probably safer than wherever you live now. I would say it is a tourist trap in the morning too if you are in the actual area around the mosque, and that probably doesn't change at night. I can't tell if you mean legitimate massages or illegitimate massages (you can tell the difference fairly easily. You aren't going to get surprised with a hand down your pants if the place has a storefront facing a road with unobstructed windows. A good rule of thumb is if the place has a woman standing outside with shoes that you wouldn't want to walk in for more than 5 minutes, the rates increase in large increments with them starting at a cheap standard massage, and you don't see anyone getting a massage in the front, then it's not a regular massage. Trust your gut.)

It takes about 15 - 20 minutes from your hotel (Hotel Parc Sovereign) to reach Kampong Glam either via foot or public transport. You can either google the route yourself or enquire the directions from your hotel's concierge The last time I visited the Malay Heritage Museum (formerly the Istana Kampong Glam), the admission was free. And don't you worry about food wise. You'll be spoilt for choice with the wide variety of cafes and restaurants along Bussorah Street. I would suggest catching an early breakfast at Kampong Glam Cafe. A lovely coffee shop where tourists rub shoulders with the locals :) Have fun in Singapore!