I would like conduct DMFC experiments. Which instrument or tester to be used for measuring 0-1000 mV voltages and 0-5000 mA current. The peak power generation by the cell is 0.5W. Is it possible to make my own set up for this experiments?
I understand from your question that you need voltage and current measurement in your setup. The measurements can be performed in many ways. If you need manual measurement than simply connect two multimeters one in voltage and other in current mode. Any general multimeters cover the required range. Another way I suggest to use multimeters with computer communication capability. You will be able to acquire data in computer for further processing as per your requirement. The general communication programs are available online or sometimes by the manufacturers itself.
You could use the Keithley 2461 which is a Source Meter instrument. This means it can supply/dissipate power and perform measurements at the same time. It is a quit expensive instrument (~ 10000 euros) but it is accurate and allows for automatic Sweeps and remote control.
You could find the old version of it (Keithley 2430) which is cheaper.
It sounds like you need two general-purpose multimeters, or, better still, a single, double-channel multimeter. If you don't already have one, buy the best you can afford and make sure it has good connectivity (USB or Ethernet). You need to have a good idea of the accuracy you require and make sure the meters you get have sufficient accuracy over the range of voltages and currents you need.
And, yes, if you're confident you know what you're doing, you could build your own based on a multi-function DAQ with some external signal conditioning. You could go that way if your bought-out budget is very low.
Find some datasheets online, work out what features you need or might be useful, select a subset and contact suppliers for quotes and advice. Suppliers usually have people available to answer your questions.