Vpanel >> Vbattery so panel acts as ~~ constant current source.
2 batteries in series or 4 batteries in series will still be << 9V so charge in the same time.
Imp < Icharge < Isc or
0.33A < Icharge < 0.43A
Say ~~= 350 mA.
T charge ~= Battery_mAh / Ichg x 100 / Battery_efficiency %
NimH CURRENT acceptance efficiency probably 80%-90%
= 700 Mah / 350 mA x 100/80 ~~~= 2.5 hours
That's in full mid-day sun with panel square on to sun.
Charge for longer than this and you will quickly "cook" the batteries.
Vbattery_max at that charge rate should probably not be more than about 1.5V/cell when charging.
Google: your_city_name gaisma
eg Bangalore gaisma gives
http://www.gaisma.com/en/location/bangalore.html
to get SSH = sunshine hours per day (= kWh/m^2/day)
Your panel will produce ABOUT 350 mA x SSH mAh per day
Bangalore example -
Half a day on an average day will be more than enough in any month - see below.
Chart from Gaisma entry for Bangalore as above.
First of all, are those numbers for the pump all from the same model? Because the range of the numbers is rather large: you say that it starts with 2 watts, nominally runs at 15 watts(?), might sink 4.5 amps at 12 volts, which gives 54 watts. And even larger numbers are calculated in your question, which probably aren't relevant.
Looks to me that even the 120 watt panel is overkill, but it can be connected directly to that pump if the pump can inded handle 24 volts, which is more than the open circuit voltage, which is the maximum voltage the panel can ever generate.
The thing to realize here is that it's the amps that turn the motor, not the volts. Volts are something that have the capability of giving amps to a load. And pushing amps through a load generates volts across the load. In your case, there's a solar panel, which is more like a constant current source, unlike, say, a battery, which is more like a constant voltage source.
When you connect the solar to the motor and there is sun, the panel pushes amperes to the load. The 120W panel looks like it might push something like 6 amps to the motor. That would perhaps generate something like 16 volts over the motor, although this number is only based on a rough feeling. That would mean that some 96 watts are dissipated somewhere in the pump - and that seems quite a lot for a pump that nominally takes 15 watts. I don't know; maybe the pump is electronically regulated somehow so that it never draws so many amps...?
All in all, I have a bit uneasy feeling about this. It would help if you could provide some more info about the pump. A link to a datasheet or a product page, maybe?
Best Answer
So, your maximum power voltage is 17.49V and maximum power current 0.57A.
It means you need load with resistance 30.68 ohms.
You can use heating wire (nickel chrome) with this resistance. Of course you have to cut wire to length you calculate from parameters of that wire.