I know that when close range characters (anyone except for Aigis, Naoto, Yukiko, Zen, and maybe Ken) attack, they do less damage when hitting from the back row or when trying to hit an enemy in the back row. But do physical skills like Toxic Slice and Teardrop also have those same restrictions? Or do they maybe act as normal physical attacks based on the character's weapon? Maybe it varies from skill to skill?

The reason I ask is because I'm trying to decide whether to use Chie or Aigis for my main physical skills user. If these all (or even some) skills are inherently close range, then Aigis would be at a disadvantage if I kept her in the back row. But if the skill range is based on character weapons, when Chie in the front row can only reliably hit front row enemies, while Aigis' ranged weapon can hit anyone.

For the record (not that it has much bearing on this question), my party so far has been P3MC, (Chie), Akihiko in the front row and Naoto, (Aigis), Yukari in the back row.

They aren't effected. Persona skills are always considered "ranged" attacks regardless of what they actually do. Bear in mind some physical skills may not be able to hit the back row in the first place, but that is a restriction on the skill not the skill user. Tons of persona physicals do "piercing" effects though which mean they hit the front row then a target in the back.

Also, yes, Zen uses a crossbow so he is ranged. He is also possibly a contender for hardest hitting straight physical attacker in the game which is all kinds of funny.

So using Chie in the front or Aigis in the back doesn't make a difference when it comes to skills? Cool. Although I guess now I'll need to figure out some other reason to choose either Chie or Aigis...

And if I do go with Aigis, I'm wondering if I should put her in the front row. She's got a ranged weapon, but she still looks like she could take hits even better than my current front row.

I could have sworn I came across some skills that my back row peeps couldn't use on opposing back row peeps which my front row peeps could. Not sure if they were physicals though.

There is a thing that says RN or ML, which I guess is "ranged" and "melee"? I suppose I should just try a few different moves with different characters from both rows and see what happens.

Well bear in mind the game itself also says Aigis is best used in the back row and her persona is all physical attacks. Think about it :P. Zen's curse attack which is also a melee move can be used from the back row.

True.

I tested this with Chie and Aigis, moving both around to the front and back, and you're right. Some physical skills can hit either row when used from the front, but can only hit the front row if used from the back. In other words, they've got a range of 2 rows and can't hit something 3 rows away.