This board is supported by a real estate related company. About the only websites that you cannot post here are real estate related websites. You can understand why.
As an initial comment: If you search this board you will find tons of horror stories regarding Singapore real estate agents. Scammers. Fools. Agents that will try to convince you nothing is available in your rent range. Agents who insist you must sign a letter of intent and give them money before the lease is signed (never do this). Agents who disappear into the wood work if you have an issue with the LL. Be forewarned that my estimate of incompetent or scamming agents is about 50 percent of the total. Do a search here and get informed about the state of real estate agents in Singapore.
As far as your questions go: It is tough times for landlords. Because of the cutback in the number of foreigners being allowed to work and a general slowing of the economy, rents have been falling. Quite a number of LL's don't want to believe that and leave their
property empty but keep this fact in mind when negotiating rent. Don't listen to landlord agents tell you the price cannot be dropped. Educate yourself on available rentals and fight back. Agents representing the landlord want to get the highest rent possible.
Second, unless you hire your own agent to find properties for you and to negotiate a deal, it is the landlord's agent who is paid by the landlord to find a tenant for him. Do not fall for any kind of deal where the agent tries to bill you as well... that activity is now illegal and you should report the agent.
Hiring you own agent will prove to be generally worthless and not worth the money. To often, the unscrupulous agents are just going to go to their agent buddies and offer to show them the place in exchange for a cut of landlord fees... plus your own, of course. One exception that has been noted in some threads here is a sliding scale fee to your agent based upon how much rent reduction she can negotiate. But, that seems to be few and far between.
Find properties on the web and in the papers. Contact the agent for viewing. Better yet, contact a landlord directly and keep the agent out of it, if the landlord is willing to work that way.
Finally, it is common practice for landlords to set a lease term that includes a provision that you will pay a pro rata portion of the agent's fees if you break the lease early. Lease negotiation in Singapore is a whole 'nuhter subject, and be aware that this provision has to be agreed to by you.