When I connect my cables from the TRS outputs to my direct-field monitors, the latter seem to be unbalanced: one monitor plays more higher frequencies than the other

You should use TRS since that is balanced just like XLRs.
Especially for long wire runs. This is if you go for XLR on the other end =
Pin 1= Sleeve
Pin 2= Tip (HOT)
Pin 3= Ring
Normally, in US equipment, 2 & 3 are inverted (3 is HOT), but you got British here, they switch the HOT pin on the XLR to pin 2.
That means that if you run this unit with US speakers your signal will be out of phase. Be careful there... I have lived this with AH boards before.
You can also use normal unbalanced cable for short runs, but I suggest keeping to standards.

It could be the type of cables you're using. Are they balanced or unbalanced?

The jacks on the end will tell you what type of cable it is.

If the metal jack (plug) has 2 circles, it's a three-conductor plug (TRS or "tip-ring-sleeve"), which means the cable is balanced. It's meant for stereo connections.

If there's only 1 circle, the plug is two-conductor (TS or "tip-sleeve"), meaning the cable is unbalanced. It's meant for mono.

There's a 3rd kind, (TRRS "tip-ring-ring-sleeve). It has 3 circles, which makes it a four-conductor plug. The extra ring is specifically made for microphone connections in 1/8 in. This is the one you would want to use for a cellphone connection, for normal operation.

But because of what you're doing, the connections and cables have to have to be specific, otherwise you'll end up with lots of noise and interference. It's much easier if you have pictures to look at, that way it won't seem so overwhelming.

This should be able to help. If not, just let me know and I'll do what I can to help you figure it out another way.

TS TRS TRRS TRRRS Combating the misconnection epidemic by Allan Tpper...

Without more information of your speakers and amps we can't really help you. The Mackie board puts out line-level signals and that should drive any connected amp or powered speaker to the full capability. Make sure you are using BALANCED interconnect lines either XLR or TRS cables. Use of TS unbalanced cables costs you 6 DB and also noise pickup. Make sure ALL your gear, amps, speakers etc are powered from a SINGLE receptacle or power conditioning module. Normally you will use the AUX outputs of the mixer by way of TRS cables or balanced lines in a snake to power amplifiers onstage which then connect to the stage monitors. If you have powered monitors the returns of the aux to the stage go to the powered monitors. A heavy duty extension cord brings power back from thee stage power to the mixer.

You will have to have an amplifeir between them since the PV12M is an unpowered speaker. The Xenyx 2442FX is likewise an unpowered mixer meaning it cannot directely drive a speaker. You will wire with a balanced line (TRS cable) between the 2442 and the amp and then from the amp to the speaker using a speaker type cable.

The half-way cord is the clue. Read up on unbalanced and balanced lines and TRS connectors.
One of these requires TRS connections and the signal is being carried on the RING of the TIP-RING-SLEEVE connector. Plugging in half-way the TIP touches the ring pickup contact. The emgs one MAY use TRS type cables and there may be a reason the signal and hot of these are reversed. If I could find schematics on all this equipment I could unravel the exact cause. You could make an adapter with a Stereo 1/4 inch plug and a 1/4 inch jack by wiring it to swap the tip and ring between them to use for connecting to the emgs guitar. ALSO verify you are using the SAME type guitar cable for both.OFTEN a TRS cable will NOT turn on the electronics when plugged into a guitar. Use an unbalanced instrument cable unless you have the XLR type output. Use of an adapter from the XLR type cable into the Boss will usually not work.

No you can't quite do this since the EQ's are right before the power amps in the signal flow. The monitor output would drive two 8 ohm speakers daisy chained at roughly 300 watts RMS... I can't imagine needing more than that for a venue that is within the capabilities of this unit.
You can drive both power amps by the monitor output by setting the mon/main function on the switch and using a short TRS cable jumper between MONITOR PREAMP OUT and the RIGHT POWER AMP INPUT jack. Drive your mains from the LEFT PREAMP OUT. The EQ's will ONLY affect the monitors. Use an external EQ if you need to EQ the mains with this connnection. Use TRS balanced cables to the main amp and CONNECT all interconnected equipment to the SAME power source or receptacle, even if it means running an extension to the mixer.

You will plug an UNBALANCED 1/4 inplug cable into the MONI jack on the front of the unit. The other end will probably need to be an XLR plug to connect to the Kustom POWERED monitor. Please note that the UNBALANCED output of the Phonic is NOT good engineering practice. The Phonic stuff is normally low-end and they don't do everything correctely, although for a small system it should work. IF you get excessive hum from using a long cable to the Kustom with a "Kludged" unbalanced to balanced cable, you MAY need to use a DI box at the Phonic end to convert the unbalanced Phonic MONI output to a balanced line (XLR to XLR) for a longer run to the Kustom monitor. You might get a 1/4 inch TS to XLR balanced plug that has a transformer in it and use an XLR to XLR cable to the Kustom. Please note that having this plug in the Phonic hangs out and is easily bent over so I would recommend using a right angle connector at the Phonic and plug the 1/4 inch TS to XLR adaoter into that so the yanking of the XLR cable won't break the 1/4 inch adapter off in the Phonic.

It is possible and depends on the length of cables you will need. If you are using a fairly long run of say 50 feet, I would put a DI box with "ground lifted" to convert from unbalanced to balanced. If the cables are short, then you can probably use a unbalanced 1/4 inch plug to XLR adapter and an XLR to XLR cable between the adapter and the speakers. The system should be safe and should NOT cause any damage. Remember to run the whole interconnected system from ONE receptacle or power source.

You didn't mention what brand powered mixer you have, HOWEVER MOST powered mixers also have a line level monitor and main output jacks. These are almost always 1/4 inch jacks. In any case you should be using BALANCED lines to the powered speakers using either XLR or TRS connectors on the ends. Please tell us what powered mixer you have so we can give you better answer regarding which connections to use. IF for some reason your mixer does NOT have line level outputs, you can use a high level Direct Box to condition the powered outputs to be sent to the powered speakers..
Also make sure ALL your interconnected equipment is powered by the same receptacle or source to avoid damaging due to ground bounce on utility lines and circuits. This often means running an extension cord from the stage where the powered speakers are along with a snake of the audio cables.

It is not clear what your configuration is. The monitor OUTPUTS are monaural. For recording you should be using the MAINS OUTPUTS and those NEED to use the the MAIN1 IF you are using TRS balanced lines, else if you record with unbalanced cables you need to use the MAIN2 outputs...

Monitor outputs are intended for stage monitors and vary ONLY with the monitor controls at each channel and the monitor sliders and do NOT vary with the sliders.