Also moving to Singapore soon but from Melb.
What I have managed to decipher to date...
The +1 generally means a maids room. If we had a similar room in Australia we would call it a store room. Its about the size of one.
Most places tend to be either fully or partially furnished. From what I have gathered, unfurnished means there is nothing including no kitchen cabinets, no stove, etc. Partially furnished means it is inclusive of whitegoods (Fridge, washing machine, Stove/cooker etc not necessarily a dryer). Fully furnished speaks for itself.
If rental is under sg$2500/mth then the agent will expect you to pay 1/2 mth rent in fees. This seemed weird to me.
1+1 lease means 1 year at a fixed price, with the option of another year based on new negotiation on rent after the first year.
2 yrs lease, (Diplomatic Clause) is a 2 year lease. If for some reason you have to leave the country (personal choice or not) then you can get out of lease after giving 2 months notice after the first year.
Unless you have lived in Singapore, it is quite difficult to get an understanding of accommodation, location etc, etc... Especially without seeing the place in person.