I will not speak to the code issue as other already have. But, I did use them when building my new home a few years ago and, for me, they passed inspection.
While the package does say they can be used for stranded wire, I did not find that they worked that easily with stranded wire (I was using some computer controlled switches with pigtails instead of screws). But, they did work. I just had to twist the strands fairly tight first.
As far as coming loose? Not the ones I was using. If memory serves me correctly, I think there is a little hole that you can push the spring up with to release the wire because it is so tight.
You're in conduit, use individual wires - they are cheaper, they pull easier, and the conduit fill on cables is terrible.
Typically we shoot for less than 3% voltage drop at rated current. Less drop is OK.
I'm fairly sure you need 6Ga wire minimum for a 60 Amp feed - given a short 30 foot run, this is also probably perfectly adequate. I'm getting 1.8% drop for 60 amperes at 240V on 30 feet (one way) of 6 Ga. Edit - Copper!
The limiting temperature rating if using THW, THHN, etc wire is generally the temperature rating of the connectors on the service equipment (breaker or panel) which is usually 75 C - even if using 90C wire, you have to follow the 75C section of the table due to the connections.
Copper .vs. Aluminum.
Copper (Cu) costs more, Aluminum (Al) less.
Copper has better conductivity - effect being, smaller wire to carry the same current. In this case, 6 gauge copper .vs. 4 gauge aluminum.
Copper oxides are conductive. Aluminum oxide is an insulator, forms quickly, and sticks very tightly to the wire. Aluminum connections need special procedures and materials to make a solid connection that won't get loose over time and overheat. These include things like brushing the wires with a stainless steel brush and an aluminum wire connection compound that coats the wire to prevent contact with air. The connections themselves must be rated specifically for use with aluminum, but most large ones will be (generally marked Cu-Al meaning they work with both, where unmarked connectors are assumed to be copper wire only.)
Aluminum connections are further complicated by cold flow, but that gets long and complicated to get into, and is supposed to be addressed by using the proper connector types. Essentially the connection gets hot, the wire swells, the swollen wire deforms, the wire shrinks, the connection gets looser, so next time it gets hotter, repeat until fire.
Best Answer
The current carrying capacity of wire and cable is determined by (1) the heat produced due to conductor resistance, (2) the high temperature limit of the insulation used, and (3) the surroundings of the wire to the degree it traps heat in the insulator (everything such as insulation thickness, conduit, proximity to a hot roof, etc.). Items (1) and (2) are characteristics of the wire. Item (3) is a characteristic of both the wire and the installation.
Even though the wires within NM-B cable are THHN wire and have insulation rated for 90 degrees C, many versions of the code, including 2011 NEC Section 334-80, limit ampacity of non-metalic cables such as NM-B to no more than that permitted with an insulation rated for 60 degrees C (probably due to heat retention by the thick outer PVC jacket, although they do not explicitly say that is the reason):
The code goes on to explicitly describe how the cable must additionally be de-rated for the installation (multiple cables in one conduit, multiple adjacent cables in an insulated wall, etc, etc.)
The differences in ampacity are all about the effect of heat on the insulation. Regarding multiple ampacities for a single wire type, there is always an asterisk somewhere describing the particular instance where the wire is to be used and which ampacity is applicable in that case.