Can I use a synthesised RNA fragment containing the amplification target to construct a standard curve for a one-step RT-PCR? Can I also use the RNA fragment as the amplification control?
We do something similar in our lab with synthetic DNA oligos (gene blocks) from IDT. They work in a one-step RT-PCR. I suggest using DNA oligo controls since RNA is vastly more fragile and prone to degradation, and if you want to use it as your control, it should be of sufficiently high quality and purity. You don't want to waste time/reagents in your runs trying to determine if your standard (control) was off/wrong (degraded) or if your samples are.
I would definitely rahter go for an in-vitro trasncript. RNA is more picky but using this you will be able to compare it as RT-efficienc migh vary and by using an in-vitro transcript you would be able to directly copare it. Otherwise the risk is high to underquantify your RNA sample in case of non perfect RT-performance
There are several research articles using synthetic DNA for standard cure generation. same as Craig Silver's suggestion, the RNA is very easy to degrade, so you have to measure the concentration of RNA including its integrity in each instrument run. In addition, your synthetic RNA would be degraded from freeze-thaw effect during storage. I would suggest you that you should use a housekeeping gene for internal/reverse transcription control, then using the synthetic DNA containing your target amplicon for absolute quantification by standard curve. the dilution of synthetic DNA in DNase-free water could stable at least 2 weeks in 4 C and the synthetic DNA stock can be preserved at -80 C for long time storage (more than 1 year for my laboratory). it's easy for you to handle the experiment.
Some additions. Short RNA fragments are not instable in general so we use them in several kits as internal control without issues. The point here is that you will not see if your RT efficiency affects your results. In addition and this is true for DNA as well as RNA standards I would not use water for dilution. If you just think your template is 500bp and you need 1000 copies/ul this means the concentration is far below 1fg/ul. I would use a buffer with carrier RNA like Quantitect nucleic acid dilution buffer.