A 5v charging system, I'll guess to charge a 5v battery, will include resistors and capacitors too. The idea is to start with a higher voltage and a regulate the ouput at 5v. Automobile battery chargers are suited for general auto battery charging, while others are designed to charge less durable, higher technology small capacity batteries. What's the capacity or Amp/hr rating of the battery?

What is the circuit generating the pulse? Digital electronics produce pulses at 5V and maybe 3.3V. 140ns eliminates many integrated latches which operate at logic levels. It's possible even a latch at 140ns will not trigger with the circuit supply voltage.  I'd use a use a two stage high frequency BJT common emitter gain circuit and a high enough frequency latch.

There is nothing wrong this stabilized 30Vdc power supply. Having not tested the orginal circuit, it must be a good design, or it would not be posted. Since it's a good design, but doesn't meet your requirements, a totally new design is needed. The engineering principle behind this design is found in many different power supplies. Can't you just buy this power supply from the website?

Integrated amplifers have become synonymous with circuit development. Their gain or their function is excellent as is shown by specification. But most designs are very large and dependent. Do you guess on which IC might be the right one?

Another thing to consider is the ability of solar panels to be used with reactive loads. If they can, the apparent power consumption will be an additional loss in power transfer. You must have a good size and expensive solar panel. I wouldn't risk in damaging it.

No. The voltage regulator can be any high current 12v regulator. A very efficient DC ro DC converter has to be used to increase the power efficiency of a circuit powered by a solar panel, and that may not even be efficient enough.

You can't mean a high current voltage multiplier can't be designed from an oscillator. Many high power oscillators use low power oscillators which again get power gain. You can't use electrolytic capacitors because their voltage rating is too low. The inverter designed using a voltage multiplier will have the AC composite and the NE555 timer will need to be decoupled so that the other voltage mutiplier can produce the negative cycle. The two circuits can be switched on and off at 60Hz.

Capacitors are good power transmission components. But electrolytic capacitors, which have the most capacitance, are low voltage. You can combine numerous electrolytic capacitors and achieve a very high current. The NE555 timer can be used or another IC or circuit.

Simple nonlinear loads can be found in many components. Most of the time, large transistor based circuits are used. Nonlinear loads are really important in circuit development.

I dont' recommend any circuits I know of. If your design is functional, it may be worth developing. There are many electronics products I have no experience with.

Diff amps are still more like opamps. The instrumentation amplifier your designing is going to be inherently poor because the voltage is too high. The problem is that the ouput will be noise. Only a fragment of the signal will remain, but it may be useful.

Having been out of school for a while, the text books are probably leaning towards more contemporary ideas than they used to. But the electronics industry has been growing massively. Just about anything your interested in is worth the study. Communications is popular, but it's diverse and is on the complicated end of electronics.

The PCB consruction for both high frequency and low frequency circuits is more complicated than that of the average use for this power supply. I would say to use a simple solder and wire circuit. Most often the problems will be the rest of the circuit. If you can fabricate a PCB, use larger conductors that will handle the current.

I don't know of any inverters that can power 220V motors. A 110V inverter is useful for powering small appliances from a battery, but it is better to purchase one because of the complexity of their design. If you can't get the motor to turn, either the motor voltage or the frequency is too low.