If you mean the little rectangular 9V batteries, they have very low capacity, around 200 mah
so wont last very long.
LIPO batteries are much better capacity wise, but the cells are 3.7 V so you need 2 in series
to power an Arduino.
But LIPO batteries need a special  balance charger if you are charging 2 or more at the same time.
With any kind of project that has a Radio Transmitter in it , as the Transmitter generally is what pulls most of the
power, its important to know just how much of the total time the Transmitter will be on.

A typical AA battery is around 2500 mah , and the battery voltage is 1.2 V if its a rechargeable
or 1.5 V if its a primary battery.
To run an Arduino you need either 5V regulated , or higher if you want to use the onboard regulator
on the Arduino board.
So you need at least 4 1.5 V AA batteries in series , or 5 1.2 V in series.
Even thats a bit marginal for the onboard voltage regulator.
With batteries in series , the same current flows through them all, so the mah capacity of the series
batteries is the same as one of them .

Whats the "device" that ultimately providing the data.
Thats what you have to support at both ends.

 Are you wanting a GSM module or a wi fi module.
They arnt the same thing.
In your original post you mentioned a GSM module.
Even an Arduino by itself wont run for 6 months on AA batteries,even in sleep mode as
The USB chip alone pulls around 15 ma ,which for AA batteries of 2500 maH will last around 7 days.
The GSM modules are the problem , power wise to run off AA batteries.
Heres the specs for a typical GSM Arduino shield.
http://www.sparkfun.com/datasheets/CellularShield/SM5100B%20Datasheet.pdf

Idles at 7 ma , on Transmit consumption anywhere from 300 ma up to 3000 ma.

What you are trying to do is not a trivial task.
You have to implement the entire USB 1.0 protocol (thats the best you can hope to achieve over wi fi) between the 2 ends
of the wi fi link.
Heres a link to the protocol spec.
http://www.usb.org/developers/devclass_docs/usbccs10.pdf

This might be of some help in implementing part of the USB spec.
http://www.obdev.at/products/vusb/index.html

Its not free though.

Most of the USB wireless extenders use custom VLSI chips to do all the hard work, which is one reason they are fairly pricey.

How long do you want the batteries to last.
Its feasable to do , but the battery life will be pretty short, less than 2 hours at best.

You really need a battery connected to the Solar Panels to provide a stable voltage.
Its not possible to know from just measuring the Solar Panels voltage when there is enough light available
to produce the current that your circuit needs.

This link will help you determine the relavant values.
http://www.daycounter.com/LabBook/BuckConverter/Buck-Converter-Equations.phtml

For Buck Converters, the Inductor must be able to handle the peak switching current without saturating.
The Peak Switching current is higher than the load current.

At 800+ Mhz , coax cable loss starts becoming pretty significant with any long length.
You need to provide details of what type of coax cable you intend to use.
RG58, which is a common type of 50 ohm cable, has a loss of approx 1 db per metre at 900 Mhz.

The problem is the 433 Mhz receiver, they are very critical on supply voltage.
They need 5V plus or minus 0.5 V.
They wont work on 6V.
The reason most likley that the coin cells work, is that they arnt designed for delivering much current, so its likley
the current the Mega8 is pulling is causing the cell voltage to droop a bit.
If you want they system to be reliable its best to run the receiver off 5 V regulated.

What type of motor does the fan have ?
If its a single phase induction motor which many fans are , you cant easily vary the speed.

Whats the power source for the wrist module going to be , as that will ultimately determine
what sort of RF transmitter / Receivers you can use.

The sensor automatically goes into standby mode at the end of the reading cycle, and stays that way until you read it again.
It draws approx 50 uA in standby mode.

MPP trackers are essentially switch mode voltage converters, with intelligent software that juggles the load on the Solar panel
to obtain the maximum output power.
There are many common algorithms used for the load juggling, but basic idea is to measure the output power from the Solar panel
and then change the load in some defined manner, and then see what happens to the output power.
Its not that hard to do, but you do need a good understanding of how to design switch mode power supplies to keep their efficiency
high.
For very small Solar panels is not worth doing,as the output power increase is at best around 30%, and unless you can source all the parts
for the tracker for next to nothing,its usually cheaper to just buy a 2nd solar panel.

What sort of Transmitter and  Receiver  are you using.
When you say the receiver is not responding, what do you mean.
How are you looking at the receivers output.
Actually measuring the Transmitters frequency needs either a frequency counter or spectrum analysis tool
which most people dont have .