Heres a little help so you can understand the problems and help you solve them yourself.
8 ) This is a filter. The gain of the filter is -(Feedback impedance)/Input impedance. At low freq, Reactance of cap(1/2*pi*FC) is high, so all current goes through the smaller 10M, hence gain = -10M/100k. At high freq, reactance of cap is low so Gain becomes - Reactance/100k. As freq increases Reactance decreases, so Gain gets smaller. It passes low freq, and not high freq. The freq at which it cuts off is 1/(2*pi*10M*0.01uf). Multiply your input 2V by the Gain at the freq your interested in, and you'll get the output waveform.
4) First work out which way is current is flowing in the arrangement when the input is at 3 different values, -10v, 0v, and 10v, then use ohms law to work out voltage drops, remember voltage across a forward biased diode is 0.7V.
5) NPN transistor with a resistor on the emitter and collector, Gain is -Rc/Re. Bias the collector so its midway in the power supply to get maximum swing. So quiescent current is (Vcc/2)/(Rc). Couple the input with a capacitor, and resistor to ground, this acts like a high pass filter with cut off 1/(2*pi*R*C).
7) Op amp negative feedback works to keep the inputs equal. So if +ve input is at ground, -ve input will also be at ground. Input impedance of a circuit is impedance to ground the input signal "see's".
Should get you started!
Megamox