In which way can I use operational amplifiers to amplify XLR signals

1. You can use any amplifier you like. You will get better performance if you use a modern $5 dual op-amp than a 2-cent/amplifier LM324. Sub-zero means nothing to me. If you want to the amplifier to have guaranteed characteristics below 0°C, then you should buy one that is guaranteed for that temperature range. Below -55°C you may have to qualify them yourselves. For temperatures down to -20°C it's unlikely that anything untoward will occur other than possibly slightly worse performance for a chip guaranteed over the commercial temperature range. A single 5V supply will impose significant limitations on the input common mode voltage. You can add pullup resistors to the output of an LM324 to get a bit more range (you probably do not want to do this on the output amplifier). Note that the left two amplifiers can saturate at either rail, so even if the output should be within range that doesn't mean that the amplifier will work properly. I presume your common mode input voltage will be close to 2.5V so this may not be a problem. LM158 and LM124 ancient designs are particularly crappy amplifiers for low level DC- large offset voltage and large offset drift with temperature.

2. See above. Offset voltage, offset voltage drift. Probably useful range of input. Closed loop gain accuracy will likely be lower too, because of op-amp gain.

3. If you could use an analog switch with your micro to auto-zero the amplifier you could improve performance. A SPDT switch is sufficient (eg. 1/2 74HC4066). Just transfer one input to be shorted to the other at ~2.5V and measure the amplified offset voltage. Average over many measurements and subtract from the measured signal.

Modern mixed signal ICs (audio processors and such - not op-amps and high end devices) mostly use a single rail power and their analog output is already centered around some DC voltage and does not go below zero, so with those kind of chips you can use the analog multiplexer as is.

But if you have a line out which is either floating or centered around zero volts, or can be something that you don't really know what it is (such as an external connector), then you must use a coupling (DC blocking) capacitor at the line out pin, and then use a "biasing" resistor to weakly pull the zero point to a suitable DC voltage between the rails. If your positive rail and ground are clean, then you can use a small resistor (something like 10K ohm) to both VCC and GND from the "other" end of the capacitor. Then you have an audio signal that sits nicely between the rails.

If the vcc (or avdd) signal is not clean enough, you must use a separate clean power source (a reference diode or good ldo) at a suitable voltage level to bias the signal to. For example, LDO output of 1.5 volts, and a 10K resistor from the signal to the LDO voltage.

At the other end you must use a similar blocking capacitor and just to be sure, weakly (100K) pull the other end to the common (ground) of the receiving line in. Depending on what the input impedance of the line in is (in the stone age it used to be 600 ohms but now it's rare to find such low impedance line in), you must determine the size of the coupling capacitor - it must be large enough that the bass frequencies don't cut off too much - because the coupling capacitor forms an RC filter together with the input impedance. 10 microfarades should be in the ball park.