In recent years, many applications have been proposed that require detection of light signals in the near-infrared range with single-photon sensitivity and time resolution down to few hundreds of picoseconds. InGaAs/InP singlephoton avalanche diodes (SPADs) are a viable choice for these tasks thanks to their compactness and ease-of-use. Unfortunately, their performance is traditionally limited by high dark count rates (DCRs) and afterpulsing effects. However, a recent demonstration of negative feedback avalanche diodes (NFADs), operating in the free-running regime, achieved a DCR down to 1 cps at 10 % photon detection efficiency (PDE) at telecom wavelengths. Here we present our recent results on the characterization of NFAD detectors for temperatures down to approximately 150 K. A FPGA controlled test-bench facilitates the acquisition of all the parameters of interest like PDE, DCR, afterpulsing probability etc. We also demonstrate the performance of the detector in different applications: In particular, with low-temperature NFADs, we achieved high secret key rates with quantum key distribution over fiber links between 100-300 km. But low noise InGaAs/InP SPADs will certainly find applications in yet unexplored fields like photodynamic therapy, near infrared diffuse optical spectroscopy and many more. For example with a large area detector, we made time-resolved measurements of singlet-oxygen luminescence from a standard Rose Bengal dye in aqueous solution.