The first two parts of your question aren't really geospatial specific, and you would need to determine how errors propagate throught the particular calculations you are performing. For example, if you are calculating distance between two points, then your error will be in units of the distance (sum), but an area will give you units of distance^2 (multiplicative effect). Any real calculations is going to have a far more complex error dependency.
I don't think number of decimal places (alone) is important - consider UTM vs lat/lon degrees - two decimal places has completely different effect.
I'd also caution that projections aren't anything like "true" - they are (at best) reasonable approximations to reality. https://www.spacecomm.nasa.gov/spacecomm/programs/system_planning/pnt/geodesy/reqts.cfm claims "the accuracy of both the International Terrestrial Reference Frame (ITRF) and the World Geodetic System 1984 (WGS 84) is estimated to be on the order of 1 to 2 parts per billion, leading to a degradation in positioning of 0.6 to 1.2 cm per year on the Earth’s surface and higher at altitude".
Reference system accuracy is also a function of time. http://www.dse.vic.gov.au/property-titles-and-maps/geodesy/geocentric-datum-of-australia-gda points out that GDA94 was once reasonably aligned to WGS84 (and ITRF), but Australia moved about a metre since then. See http://www.quickclose.com.au/stanawayssc2007.pdf for more detail on this example.