Is there an absolute minimum intensity level to the stimuli we can perceive?
There are limits to what a sensory system can detect, which is called the detection threshold. To determine the detection threshold psychophysical methods can be used. A straightforward way to determine the detection threshold is with a yes/no task, where the subject receives stimuli with various intensities. An arbitrary point, mostly the 50% correct-rate, is then defined as the detection threshold. At this point, the subject correctly detects the stimulus 50% of the times. The response curve in a psychophysical task typically takes the shape of a cumulative function such as the one shown in Fig. 1. 

Hence, the detection threshold is an arbitrary point, because people are not machines and show variability in their decisions. The detection limit of, e.g., electronic devices is much more precisely defined. The exact values of the detection limits depend on the exact stimulus (visual, tactile etc.) and depend highly on the exact stimulus. For example, in the visual domain the detection limit of light depends on the color, the location in the retina tested, dark adaptation etc etc, and in the tactile domain static pressure stimuli have a different threshold than vibratory, different body parts have different thresholds etc. etc.    


Fig. 1. Psychometric curve showing 50% threshold of a visual stimulus. source: Webvision

Training to lower the detection threshold (i.e. improve detection limits) is indeed possible (Sterr et al., 1998).  

Reference
Sterr et al., J Neurosci (1998), 18: 4417-23