The biggest issue with running the 26AWG wire outside the jacket, separated is that the wires are really small, and the insulation really thin. This makes them very prone to getting nicked and shorting out, or breaking. That's why I typically use at least 22 or 20AWG in the car. If I do use smaller, I leave it in its outer jacket. You might want to look into picking up some heavier wire for the bulk of the run, and hook it up to an inch or so of the 26awg with the phone connector attached. This hookup wire would be fine:
RadioShack.com - Cables, Parts & Connectors: Wire: Hookup wire: 75-Ft. UL-Recognized Hookup Wire (22AWG)
If you have just a perf board w/ holes individually clad in copper, then yes, you put two pins through adjacent to eachother, then "bridge" the two with solder. If you don't have a lot of experience, it may be easiest to bend the legs of the appropriate components and/or jumper wire together and get the solder to stick to the copper and components.
Where are you seeing "a T in a wire"?
The 7805 is typically in what's known as a TO-220 package, with the heat sync on the back. From the front (with the writing), it should be oriented like this:
On the buttons, use a multimeter to test, but each pair of legs are connected to eachother. You can either use one of each or both, but be sure to get the right ones.
Shorting D2 and D3 with solder is fine. Wire to D2 to D3 is electrically equivalent to wire to split to D2 and D3.
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Oh and PM me if you need more help on this type of stuff - its not very constructive to this thread, its just general circuit building. Glad to help, just don't want to clog up the thread with unrelated stuff...