I see a lot of conflicting information regarding undertunic/cote length. According to The Medieval Tailor Assistant, nobility would wear their cotes/undershirts to their ankles, but I don’t see how someone could fight with your clothes all the way down to your ankles. Plus, all the effigies and manuscripts I could find show the heraldic surcoat by the knees with no sign of clothing underneath. I’m leaning towards buying a woolen replica of the Bocksten tunic, but that reproduction only goes mid calf.

When in doubt, go with the evidence. In this case, while there is some evidence to suggest cotes that extend beyond the knees being worn by high ranking men in battle, military dress is different to civilian dress.

I struggled to find a historically accurate type of headwear besides a coif worn by men mid 13th century. Looking at the Maciejowski Bible, none of the nobility/knights are wearing any kind of hats, only serfs and one Jew. Researching headgear fashion in this time period revealed tons of documentation on women’s hats but nothing for men. I know about the bycocket, but I haven’t found any evidence of it existing mid 13th century.

Unquilted coifs were the fashion in the period you're looking at. The men are mostly shown bareheaded because, apart from letting you see their lovely flowing locks, headwear wasn't mandatory for fashionable men yet.

Do I HAVE to wear a secret helmet? Going off of my last question, I’m going to look like a bobblehead with how fat my head is, and I’ve read that in this time period, knights who wore greathelms forwent secret helmets. It also cuts down on costs for me….

Nope! Secrets weren't so much secret as worn with a coif over the top as opposed to under them. I'm sure that some wore them under larger helmets but it was by no means mandatory.

Another point of contention: integrated vs separated maille coifs. I know that rectangular shaped coifs became a thing mid 13th century, but I’ve seen some insist that separate coifs were more common than integrated, as coifs were tucked under surcoats for aesthetic reasons. However, looking at the Maciejowski Bible, there’s knights with no surcoat and no sign of a separate coif in the entire collection.

When in doubt, follow the evidence. Integral hoods are fine (and so are separate ones!).

I'm afraid I can't really help with questions 3 and 6, so a reenactment subreddit is your best bet.

In all honesty, you've done a very good job researching all of this, and I applaud your decision to abandon the stereotypical aketon in favour of just a cote (which the visual evidence overwhelmingly supports). I would, however, recommend that your cote be lined since, if you look closely at the Morgan Bible and other sources from the period where the inside of the cote under the armour is shown, they're all lined. I'd recommend having fairly heavy wool fabric on the outside and lighter wool or linen on the inside. That may end up being a custom job, though, so it's up to you. Just a thick woollen cote should do the trick.

I should also note that a kettle helmet would be entirely in keeping with a mid-13th century knight (especially in Scandinavia), and that plenty of knights in the Morgan Bible aren't wearing full helmets, but iron caps over/under mail coifs.

I can't answer all of your questions, unfortunately, but I can point you to some information that might help.

The Danish army that sacked Gotland and won at Mästerby and Visby 1361 did include at least some mercenary knights Bavo or Schelto (both are candiates as their fates are unknown) Roorda died at the battle of Visby and was tossed into the mass graves along with the ~1 800 peasant milita and the Danes and other mercenaries that died in the battle, with his armour still on.

He wore a coat of plates that were in design very similar to what the Gotlander peasants wore - however, the studs fixing the plates to the inside of the leather (or maybe in his case, velvet or other finer material) were elaborate brass or bronze "buttons" in the shape of the heraldic symbols of the Roorda family.

Image of the armour at the Swedish museum of history.

It is possible that the knight did not wear a tabard over his armour as such elaborate buttons/rivets would be wasted if they were covered.

Also, ss you can see, he also wore a cervelliere - probably beneath a great helm. While coifs are common in the mass graves of Visby, helmets are not, and it is speculated that when burying the dead, the locals or the Danish army (it is not clear who did the burial) were in a rush since the bodies were rotting quickly in the hot summer sun and only took armour and weapons that could be quickly and easily removed - such as helmets, but not coifs or coat of plates. We know the weather was hot, warm and dry since the bogs that normally would protect the positions at Mästerby was crossable by the Danish army and it was noted that it was due to the hot and dry summer. At least one Danish casualty was buried with a pouch full of both Danish and Swedish silver coins, the Danish part probably from when he signed up and the Swedish part from the looting of Öland that the Danish host spend some time on before continuing to Gotland.

The Roorda knight seem to not have been wearing a coif - perhaps he wore padded cloth such as this instead.

You can read more on the armour found in the Visby mass graves in Bengt Thordemann's writings. At least one of them are available in English under the title "Armour from the Battle of Wisby, 1361".