A serviced apartment consists of a living room, kitchen and 1 or more bedrooms, is furnished and is cleaned daily just like a hotelroom. When new people arrive they usually either stay several weeks in a serviced apartment or in a hotel to look for accommodation - a serviced apartment would give you some more space, when you come with your girlfriend.
Dining out is great in Singapore and the national hobby! There are restaurants EVERYWHERE and most of them are very cheap compared to Europe. You also have hawker stands and eating houses (open air), where several stands are combined and you can order anything from Chinese to Indian food for very little money. How about eating soem nice curries in little India at 11pm? Restaurants are open long hours (mostly) and shops open from 10 or 11 am to 10pm - every day! As mentionned before, alcohol is extremely expensive in bars, restaurants and in the supermarkets as well. An average bottle of wine costs $20-25 in the supermarket!
On the cultural part, you might find that Singapore doesn't have that much to offer as Germany. But, theatre, music, museums, eveything is here. There is an online booking agency called Sistec - why don't you check out their website for ideas?
Cinemas are abundant and cheap.
And for the rest, there are a lot of destinations within easy reach of Singapore: islands in Malaysia, Indonesia (for a weekend get away) and Thailand, cities/countries like Hong Kong, Bangkok, Vietnam, Cambodia, etc. etc
You can fill your days here travelling! You'll love it!
Now that it's still summer in Europe I would buy some extra sommerclothes, as you might find it difficult regarding the sizes. there are European sizes around, but limited. I have a size 38 and have problems, especially when it comes to buying things with sleeves -asian shoulders aren't broad...And have your friend buy herself underwear before coming here, as almost everything is polyester and padded....if she already finds her size.