This question is really two questions. The direct question is whether a petrified creature is capable of using telepathy; but the implied question is whether a petrified creature is conscious. If the creature is not able to think, then there are no thoughts to transmit.
The implied question has been asked before:
Does a petrified creature stay conscious (and ...
No, they cannot
And I'm basing this mostly on this part of Petrified:
The creature is unaware of its surroundings.
This line is also present in the Unconscious condition and represents the Wizard's senses being shut down.
It does not make any exceptions for special senses, it just says you're not aware of anything going on outside your body. That means you ...
One point that is unclear from those rules is whether telepathic communication is considered to be speech under the rules of D&D 5E. That is answered in the rules of a feat from Tasha's Cauldron of Everything:
You can speak telepathically to any creature you can see within 60 feet of you. Your telepathic utterances are in a language you know, and the ...
There are reasons to apply both the Frightened and Clumsy conditions
The Flamboyant Cruelty feat:
You love to kick your enemies when they're down, and you look fabulous when you do. When you make a melee weapon Strike against a foe that has at least two of the following conditions, you gain a circumstance bonus to your damage roll equal to the number of ...
It breaks the restrainment
Of course, your GM has the last word on this. But if you are a GM looking for guidance, I'd strongly suggest to rule that the restrained condition (which was caused by a spell like Entangle, Maximilian’s Earthen Grasp, Evard’s Black Tentacles or Web) ends if the target somehow leaves the area that caused restrainment, may it be ...
The idea of mind blank is that it prevents any thoughts/ emotions from going through your skull. Not exactly sure how someone affected by the spell still moves, but that’s not what you’re asking.
If it blocks all emotions, then frightened would fall under that umbrella, wouldn’t it?
There's a rule in 3.5e that a specific rule trumps a general rule. You can find that rule in the Rules Compendium, on page 5, "Order of Rules Application."
There is a general rule that supernatural abilities cannot be dispelled, found on page 314 of the Player's Handbook:
Supernatural abilities are not subject to dispelling, disruption or spell ...
Yes, the paralysis can happen only on a hit.
This is explained in the introduction to the Monster Manual (p. 10-11), under "Melee and Ranged Attacks":
Hit. Any damage dealt or other effects that occur as a result of an attack hitting a target are described after the “Hit” notation. You have the option of taking average damage or rolling the damage;...