You will be far better off using a small battery.
The battery is not for running the Micro over the night, but is there to ensure that in low light in the morning when the Solar Panels voltage rises
sufficiently high to start the ATtiny, there is enough current available to run it.
Solar cells dont have a linear voltage / current relationship.
The voltage with no load rises at a logarithmic rate whilst the current capacity rises at a linear rate for a given illumination.
What happens with no battery, is that the solar voltage will rise quickly to above 5 V , which will cause the 7805 to start operating, but the solar cell has no capacity to deliver any current , so the voltage immediately collapses, and the Micro stops.

Ive made a number of remote operated devices which run off Micros In my case using PICS not Arduinos , but the principle is the same.
You need to know the daily power draw of the device to be powered.
You then need to know the worst case sun hour value for the middle of winter, usually around 2 - 3.
You then have to allow for multiple days of cloudy weather , usually 5 days is a good compromise , but varies somewhat depending on your latitude.
You can then size the battery and the solar panel to suit.
Try and reduce the power draw of the device to an absolute minimum when its not doing anything useful.

You need to know a lot more about the Transmitter.
How does it send data, what type of modulation is used.
Without an oscilloscope, this will be very difficult to do.

The other factor thats missing from the demo is how much power was put in to spinning up the flywheel
compared to what was stored.

Whats the motor going to be powering?
For how much of the day will the motor be running?
Do you want the motor to run in the middle of winter?
All these factors are needed to size the solar panel.

The latency you are seeing is largely caused by the encoder / decoder chips you are using, mainly the decoder.
Its inherant in the way that they work.
You will need some other method for 40.

You can buy wireless USB extenders, which will do what you want.
Be warned though, these devices are very expensive.
http://www.kvmstuff.com/extenders/usb/wireless-usb-2-0-extender.html

Software Serial uses the CPU to calculate the timing of the bits , so it can either receive or transmit but not both at the same time.
When you are transmitting a character, any incoming characters will be lost.
You need to use the hardware Usart in the Micro.

You need a CRO to test the sensor.
Until you verify that the sensor is actually working properly, theres no point in trying to write code to test it.

Look at using a SC2262 and a cheap 433 Mhz ASK transmitter to send your PIR data.
They can send 4 bits , which allows for 16 differant states.
You will need a SC2272 to decode the data.

You need to test the Sensor to make sure its operating properly.
The Sensor is a 1 wire sensor which uses bidirectional data transmission on the data line.
If you pull the data line low for 20 ms and then release it , the sensor will send a binary data stream
which comprises 5 bytes of data.
The sensor normally sends nothing until you ask it to send.

Many routers with Nat and port forwarding wont allow an external connection , if it appears to be coming from
inside the LAN.
So, to test that your port forwarding works, you have to test it from outside your lan.

The problem with running USB over wireless is meeting the USB speed standards.
USBV1.1 which is the slowest, requires 12 Mega bits/sec which is viable using wireless but
very hard to implement.
You can buy wireless USB extenders , but they are expensive .

Many of the common 2 X 16 LCD display use this chip.
Does anyone have any ideas of how to reduce the power consumption of the display.
Most of the common displays require around 1 - 1.5 ma without a backlight yet the HD44780 controller chip specs require only 150 ua .
I dont know where the rest of the power goes.
The display Im using only changes its value around once every 1 1/2  minutes so data writes dont occur very often.
Trying to make a small battery powered Temperature sensor , and 1.5 ma
draw kills the AAA batteries.

Do you actually want to make the sensors , or do you want to use existing commercial sensors.
You may be interested in this project.
http://wmrx00.sourceforge.net/
Its called Weather Station data Logger and it uses an Arduino with a custom shield to simulate an Oregon Weather Station Console and allows
PC monitoring of a wide range of Weather conditions.
It can measure Humidity, Temperature, wind speed & direction , UV , Rainfall,Barometric Pressure.
Ive built 2 Arduino based Weather Shields, and Im now in the process of making my own Temperature / Humidity Sensors using DHT22 sensors.