Show us what you have achieved so far. Our policy is not to do other's homework, but guide them to find the solution themselves. That is from experience the most effective way of supporting you. Trust me.
1) That should be easy as no propagation delays are involved in a truth table.
2) Some information is missing here. Presumably you are supposed to use the 74xx series of logic gates. Note that there are several variants, bipolar and cmos and different speed grades. For the next step to be meaningful you should know which IC family to use. Next find the right ICs (inverter, nand), name them and select suitable pins to build the above circuit. For the purpose of this task you may ignore the other gates and power supply pins which in a real circuit would have to be handled.
3) Obviously you are supposed to build this circuit (e.g. on a breadboard) and measure the behavior. Note that in this case you'll have to add bypass capacitors (typ. 100 nF) across the power supply pins of the ICs. Also you'll have to tie unused pins to a defined logic level, either high or low, to avoid unpredictable behavior (e.g. oscillations).
