Freedom of Movement explicitly disallows the application of two conditions to the subject of the spell, namely they can't be paralyzed nor restrained.

Stunned is also a condition. It is not listed under FoM as disallowed. Stunned also does not reduce the target's speed. It states that the target can't move, whereas other conditions, as you noted yourself, explicitly state an altered speed value.

The paralyzed condition is almost the same as the stunned condition, the only differences being that 1. a paralyzed creature can't even speak falteringly, 2. attacks targeting a paralyzed creature and coming from an attacker within 5 feet of the paralyzed creature are critical hits. Paralyzed inflicts another condition, incapacitated on the target. So does stunned. Stunned does not inflict paralyzed on the target. FoM explicitly disallows paralyzed, but it does not mention stunned, ergo FoM does not protect against stunned, nor against spells that apply stunned, such as Power Word Stun. Considering there's no Power Word Paralyze and no Power Word Restrain, this seems to be a conscious design choice.

I'm not sure I like this, but this is how I read RAW: FoM does not allow movement when its target is stunned regardless what applied said condition to its target (and no matter that stunned is a weaker version of paralyzed.)

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RAI I think the reasoning behind this is that stunned affects your mind, not your speed. Your speed is the distance the creature can cover. When stunned, its speed is the same, only the will to cover the distance unaffected speed would allow it to cover is impacted. (Also, the word "move" in the definition of stunned covers not just the movement of the legs or similar which allows the creature to go some distance. A stunned creature doesn't gesticulate, etc either. At least in my interpretation.)

(PHB 5e 1st printing, 2014, no errata, pages 244, 291-292)

Yes, you still get paralyzed

...because the effect causing the paralysis is not magical.

To determine whether an effect is magical or not, we refer to the Sage Advice (page 17) ruling on a dragon's breath weapon:

Determining whether a game feature is magical is straightforward. Ask yourself these questions about the feature:

• Is it a magic item?
• Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
• Is it a spell attack?
• Is it fueled by the use of spell slots?
• Does its description say it’s magical?

If your answer to any of those questions is yes, the feature is magical.

The answer to each of these questions is no, so the paralyzing effect of the grell's poison is not magical, and is therefore not prevented by Freedom of Movement.

That being said, the spell is not totally useless against grells as it enables a victim to use 5 feet of movement to automatically escape from a grell's grapple.