All the help with TSC, Here. Start I:

#0090
<MNA<CMU0000<FAI0000<END
#0091
<MNA<CMU0000<FAI0001<END
#0092
<MNA<CMU0000<FAI0002<END
#0093
<MNA<CMU0000<FAI0003<END
#0094
<MNA<CMU0000<FAI0004<END





#0100
<FLJ1563:0101
<KEY<SOU0011<ANP0100:0000:0002
<FAO0004<TRA0016:0094:0032:0002
#0101
<PRI<MSGIt won't open!<NOD<END


#0300
<KEY<MYB0002<WAI0020
<MSGWe, the Pignons,
aren't happy with you!<MYB0004<NOD<CLR
YESSS! WE REMEMBER YOU!!<NOD<CLO
<CNP0400:0313:0002<MYD0000<WAI0030
<MSGTHIS IS WHEN YOU PAY!<NOD
RECREANT!!<NOD<CLO<FL+1563<FL-1560<DNP0300<CMU0004<BSL0400
<END

#0400
<KEY<ANP0400:0500:0000<WAI0050<CNP0400:0004:0000<DNP0400<FL+1560<FL-1563<END

#0500
<KEY<SOU0015<MSGOpen the chest...<NOD<WAI0010<CLR
<GIT1023<CMU0010Got the =Booster 2.0=!<WAI0160<NOD<CLO<DNP0500<FL+0850
<MYD0000<WAI0050<MSGUmm... And...
The mimiga that was
Cleaning here??<NOD<CLO
<END

Why this doesn't work?? The fight starts, but Ma Pignon doesn't move and don't take damage (And don't cause damage)...

 

Simple, you're just not running <ANP. When you're using <BSL that's just the event that runs when the boss dies.
Just put <ANP0400:0100:0002 in the script and it'll start doing the boss fight patterns.

 

Hello! That works fine! But I have another problem:

#0300
<KEY<MM0<WAI0010<MYB0002<WAI0010<MYB0002<CNP0200:0013:0000<MYB0000<MYD0000<WAI0010
<MSG<FAC0025Quote!! Look at that!<NOD<CLO
<MYD0002<CNP0350:0012:0000<ANP0350:0000:0000
<MSG<FAC0000Oh! So we have a new visitor!<WAI0050<CLR
WAIT!!! YOU AREN'T DEAD!<NOD
GET OUT OF HERE!<NOD<CLO<CMU0004<CNP0350:0068:0000<BSL0350<FL-0851<DNP0300<END

#0350
<KEY<CMU0000<CNP0350:0012:0000<ANP0350:0012:0040<MSGOH!<WAI0050<NOD<CLO<WAI0050
<ANP0350:0000:0000<ANP0350:0010:0000<CNP0200:0000:0000<DNP0350<FL+0851<END

Right after the fight ends, the NPC doesn't animate; it just freezes. The fight itself works perfectly, but this detail ruins everything. It's worth mentioning that the entity is empty, and I converted it into a Balrog in the code. I also tried not converting the boss Balrog back into a normal Balrog at the end, but the same thing keeps happening.

 

Hello! That works fine! But I have another problem:

#0300
<KEY<MM0<WAI0010<MYB0002<WAI0010<MYB0002<CNP0200:0013:0000<MYB0000<MYD0000<WAI0010
<MSG<FAC0025Quote!! Look at that!<NOD<CLO
<MYD0002<CNP0350:0012:0000<ANP0350:0000:0000
<MSG<FAC0000Oh! So we have a new visitor!<WAI0050<CLR
WAIT!!! YOU AREN'T DEAD!<NOD
GET OUT OF HERE!<NOD<CLO<CMU0004<CNP0350:0068:0000<BSL0350<FL-0851<DNP0300<END

#0350
<KEY<CMU0000<CNP0350:0012:0000<ANP0350:0012:0040<MSGOH!<WAI0050<NOD<CLO<WAI0050
<ANP0350:0000:0000<ANP0350:0010:0000<CNP0200:0000:0000<DNP0350<FL+0851<END

Right after the fight ends, the NPC doesn't animate; it just freezes. The fight itself works perfectly, but this detail ruins everything. It's worth mentioning that the entity is empty, and I converted it into a Balrog in the code. I also tried not converting the boss Balrog back into a normal Balrog at the end, but the same thing keeps happening.

I don't know why it would do that, but It may be <ANP0350:0012:0040 which is strange, because there's no animation for the Balrog(cutscene) NPC that's number 0012 and any direction after 0004 just makes the NPC face another NPC, I'm assuming you were trying to use direction 0004 since that would make the NPC face the player. It could also be the <ANP0350:0000:0000 which is pretty strange too considering you have a <ANP0350:0010:0000 right after that and just putting <ANP0350:0010:0000 would grant you the same result.