Context. The Large Interferometer For Exoplanets (LIFE) initiative is developing the science and a technology roadmap for an ambitious space mission featuring a space-based mid-infrared (MIR) nulling interferometer in order to detect the thermal emission of hundreds of exoplanets and characterize their atmospheres. Aims. In order to quantify the science potential of such a mission, in particular in the context of technical trade-offs, an instrument simulator is required. In addition, signal extraction algorithms are needed to verify that exoplanet properties (e.g., angular separation, spectral flux) contained in simulated exoplanet datasets can be accurately retrieved. Methods. We present LIFEsim, a software tool developed for simulating observations of exoplanetary systems with an MIR spacebased nulling interferometer. It includes astrophysical noise sources (i.e., stellar leakage and thermal emission from local zodiacal and exo-zodiacal dust) and offers the flexibility to include instrumental noise terms in the future. Here, we provide some first quantitative limits on instrumental effects that would allow the measurements to remain in the fundamental noise limited regime. We demonstrate updated signal extraction approaches to validate signal-to-noise ratio (SNR) estimates from the simulator. Monte-Carlo simulations are used to generate a mock survey of nearby terrestrial exoplanets and determine to which accuracy fundamental planet properties can be retrieved.Results. LIFEsim provides an accessible way for predicting the expected SNR of future observations as a function of various key instrument and target parameters. The SNRs of the extracted spectra are photon-noise dominated, as expected from our current simulations. Signals from multi-planet systems can be reliably extracted. From single epoch observations in our mock survey of small (R < 1.5R Earth ) planets orbiting within the habitable zones of their stars, we find that typical uncertainties in the estimated effective temperature of the exoplanets are 10%, for the exoplanet radius 20%, and for the separation from the host star 2%. SNR values obtained in the signal extraction process deviate less than 10% from purely photon-counting statistics based SNRs. Conclusions. LIFEsim has been sufficiently well validated so that it can be shared with a broader community interested in quantifying various exoplanet science cases that a future space-based MIR nulling interferometer could address. Reliable signal extraction algorithms exist and our results underline the power of the MIR wavelength range for deriving fundamental exoplanet properties from single-epoch observations.