A good free option mentioned is digiCamControl, an open-source tethering and camera-control program for Nikon DSLRs. It was suggested as having many of the features of Nikon Camera Control Pro, so it’s the closest match to your request for freely available software.

Other options mentioned were ControlMyNikon, which includes a timelapse feature and can be combined with bracketing, but it was described as a free trial, not free software. Nikon’s own Camera Control Pro was also referenced, again as trial/paid software.

If your main goal is simply reliable time-lapse shooting, one answer suggested using a hardware interval controller such as the gentLED-Auto instead of tethering to a laptop. That can be simpler in the field and avoids carrying a computer.

For the uneven timing problem: if shutter speed becomes longer than your chosen interval, the actual time between frames will increase no matter what software you use. To keep timing consistent, use settings that prevent shutter time from exceeding the interval, or choose a longer interval.