I am assuming you are sending the sensor data some distance. May not be the best but easily available is cat5 networking wire. Ideal wire probably has twisted pair with a shield, just enough conductors to get by. You may be able to find some audio wire set up this way.
If you can some processing of the sensor data prior to transmission can help. For example converting to a differential signal, or taking a voltage and converting to a frequency.
It is a long question, but better than a short one, as you've shown your own research.
1) Solar cells. If you're stacking your own ones, stack 9 of them and get the 4.5V of the original circuit.
2) Battery charging. Batteries are the only thing you've left out of your spec. This is an area where the circuit design relies on cutting a lot of corners. In theory it might be out of spec, if you were to put 4.5V at 280ma through AA NiMH cells indefinitely. In practice, you don't get full sun all day, you'll be using it indoors, and you're not going to get optimal power transfer from the cells, so this isn't going to cause problems.
3) Diode. It's just a regular diode, not a zener. Current through it is actually determined by the battery and right hand side circuit, not the solar panel - the transistor is off when the panel is generating electricity. The original 1N914 will be fine. 1N4004 will also be fine.
4) Resistors: not a precision component here, use whatever meets your cost constraint. 5.1k for 5k is fine.
5) Wire: not critical. Your ebay link looks suitable. Thinner is better for the toroid.
6) Transistors: stick with the exact part numbers. Design may rely on specific parameters.
7) LED: again, this circuit relies on cheating. Normally a white LED won't run from two NiMH cells. The joule thief part provides a boost converter that gives small pulses of higher voltage. It doesn't have the capacity to provide a lot of current at that voltage. In combination with the pulsing this means there should be no risk of damaging it.
(A proper analysis of this circuit would be good, if nobody else supplies one I'll do it in a few days).
Best Answer
Adding a length of wire to each device will increase their resistance, but generally no more than 20 ohms or so depending on the gauge of the wire.
For a button using the internal pullup the overall resistance must be less than \${{20\text{k}\Omega⋅0.3}\over{0.7}} \approx 8.5\text{k}\Omega\$ or so in order to reliably register a low. Adding 6 feet of wire (3 feet towards, 3 feet back) is unlikely to cause the resistance to increase that much.
The pressure sensor is a variable resistance device however, and as such may require recalibration when connected to the wires if the actual value is used rather than just using it for presence sensing.
Also note that longer wires pick up RF more easily, so you should consider twisting the pairs connected to the device (or using twisted-pair wire in the first place) and using ferrite beads/toroids and/or common-mode chokes to suppress the disturbance caused by the RF, especially in an electrically noisy environment..