NI-DAQmx has a "simulated driver" feature. In the case of an AI, the returned signal is a noisy sine. Is it possible somehow to change this behavior in order to have any type of the signal?
And if not, are there some alternatives to simulate hardware?
I do not think it is possible to control the signal returned on a simulated device. A DAQmx simulated device is intended to allow you to check your data acquisition code works without having to have the actual hardware present as part of the development process.
If you need to provide a simulation of hardware with real data then using LabVIEW you could provide a vi that calculates (or load in) the required signal and passes this out to the main program. I have used this approach to provide a repeatable test for debugging by running the actual hardware and logging real data to a file then re-running the test with real data.