Electronic – this component in the picture

1) The article says T5 serves as a surge protector. But if the gate is connected to the bottom of RS (RS-SEL in this schematic), wouldn't the Vgs of the JFET be 1V? Therefore, the FET would never turn on under normal conditions, which kind of defeats the current source? I'm obviously missing something.

They're pulling a bit of a trick here — a JFET can also function as an ordinary diode. For example, look at T9 down below. If a positive surge is applied to K2, the gate-channel junction of T5 will be forward biased, which connects it directly to the output of the opamp, a low-impedance point.

The advantage of doing this is that in normal operation, T6 has very little leakage and very little capacitance, so that it doesn't disrupt the low-current settings.

Remember that a JFET is a depletion-mode device. It will conduct current unless the gate is driven more negative than the channel (relative to either the source or drain terminal) by the specified threshold voltage. With a V_GS of -1V, the FET still conducts. The drain-source resistance doesn't upset normal operation because of negative feedback, IC6 will raise its output voltage to the level required to force the desired current through R_S.

2) According to the article, all of the source current from IC6 travels through R59 as long as the user-selected current is 100uA or less. I believe I understand that because at 100uA, Vbe of T6 would be 360mV, which is less than Vbe(on) for T6, so T6 would be off. But wouldn't R59 contribute a very large error in series with R28? The combined resistance of R59 and R28 is 13.6k, which would result in a current of 1V/(10k+3.6k) = 73.5uA. That's pretty far from 100uA.

No, because R59 is inside the feedback loop for IC6, the opamp automatically compensates for its effects.

3) For user-selected currents above 100uA, how does R59 and T6 affect the voltage going into the resistors downstream? Wouldn't they contribute significant voltage drops that mess up the 1V reference calculations? I can't figure out an intuitive feeling for how the resistor and transistor work together here.

Again, because of negative feedback, when T6 conducts, IC6 reduces its output voltage to maintain the correct voltage across R_S.

The general principle is that components between the output of the opamp and the feedback point don't matter (within certain limits), because the opamp will act to reverse their effects and maintain the desired voltage at the feedback point. It can be tricky sometimes to understand exactly where the "feedback point" is in some circuits. In this case, it is the node labeled TP6.

This is some sort of RF test connector with a built-in switch. Possibly an MS-156 or MS-147. There is a trace going under the connector from the bottom, and another one from the top. One side goes to the radio in the phone, the other goes to the antenna. Generally the test connector is installed so that when something is plugged in, the antenna gets disconnected and the external connector is connected to the radio in its place. This allows easy testing of the radio during assembly to ensure that everything works correctly. This is necessary because if the antenna is not bypassed, the whole phone would need to be placed in a faraday cage to isolate it. My phone (a galaxy S3) has three of them under small round stickers.

They're not really designed for use with external antennas, but that doesn't mean it's not possible, just not convenient. Generally they're designed to work with pogo pins in an automated tester, it may be very difficult to find the correct adapter. And then you would need to know what frequencies the radio needs to use, and find an antenna that wil work across those frequencies. Modern smart phones have radios for GPS, Bluetooth, and Wifi in addition to the cell network radios LTE, GSM, Edge, 3G, etc. These radios operate in different bands and in some cases share the same antenna. There may also be complex RF switching to select the correct antenna and/or switch antennas on the fly, complicating the process of properly adding an external antenna. You may need more than one antenna to get everything to work correctly.

From looking at the images of the S4 in ifixit, there is definitely more than one antenna. Samsung does an excellent job integrating everything, though, so they are not very obvious. Looks like there are at least 4 antennas in the back cover - two on the top right, one on the top left, and one at the bottom. You can see two of them after taking the battery cover off; they are under the two small plastic covers on the sides at the top. Then there is another one that curves around the inside of the top right corner. Then there is at least one more down at the bottom with the speaker.