I'm much confused about US customary units so I want to ask a lot more questions under single question.First how standard units, in US customary Units, of force time and length are defined as second or mass etc have an appropriate standard definitions in SI. Second why mass is measured in two units i.e. slug and pound-mass, is this one has some significance. Can we say mass in US customary units is an analogue to weight in SI? Being an engineering student I want to have a strong concept of units and different systems of units. If someone can provide a good reference it will be most welcomed, thanks in advance.
I'm unclear on exactly what you're asking, but most (all?) of the US customary units are ultimately defined in terms of SI units. As an example a US inch is defined to be exactly 2.54cm.
Mass in US units is still just mass. The only real complication is the fact that the "pound" has historically been used both as a mass and as a force (where it is the force equivalent to the same mass under one $g$ acceleration). The old base unit of the avoirdupois pound is now defined as a specific fraction of a kilogram.
I don't know of any ways that time has been defined differently in the US system. A second is just a second.
In the SI system of measurement, one Newton of force accelerates a 1 kg mass at 1 m/s^2. This is very convenient, as there is no "factor" that you have to worry about when doing force, work, and energy calculations.
In the U.S. customary units of measurement, the unit of force is the lbf, or pound-force. The unit of mass if the lbm or pound-mass. One lbf accelerates one lbm at 32.2 ft/s^2, which is not convenient. This means that the numerical factor of 32.2 shows up a lot in U.S. calculations. Thus, density must be calculated in slugs/ft^3, which is lbm divided by 32.2, and further divided by volume.
The U.S. was supposed to convert to the metric system in approximately 1975 (which is what I was told when I was in high school). Obviously, the conversion hasn't been made, and more obviously, will never be made. This means that you, and all of my AP Physics C students who plan to do engineering in the U.S., will have to become very proficient at converting back and forth between U.S. units and metric units (which is occasionally a real pain in the rear end). The best advice that I can give you is to work extra problems in this area such that you become accustomed to properly doing conversions between U.S. units and metric units. Also, if you are given the choice, work strictly in SI units, which are MUCH more straight-forward (in my opinion).