The aluminum base of tea-lights are technically recyclable but they are so small that they are unlikely to get recycled as they cannot be baled (ie they fall through the cracks). So unless you want to clean it and sneak it into, say, an aluminum can for recycling, chuck it.

Are candles a fire hazard?

It is safe to put old candles in the trash. The flash point of wax is ~200°C - ie the temp at which it will ignite (in the absence of exposure to an open flame). It is highly unlikely the trash bin or truck will get to this temperature. So it is not considered flammable in these conditions. 

It can be fun… but it is also quite messy. It requires sacrificing a cooking pot and investing in candle wicks. 

There are a number of places where you can get your candle refilled in Singapore including Candlescape Foundation  and Houghton and Gough. But do note that these are businesses that need to make a profit to cover expenses. Using these services may cost more than buying a new candle.