Can a script check the specifications of a player

You can detect if the player is on mobile/pc, what their fps is, etc. I suggest doing a bit more research next time.
To calculate people’s fps use RunService.RenderStepped this should be done locally.
You can calculate it by doing the following: (there are multiple ways to calculate it this being one of them)

local fps = 0
local RunService = game:GetSerive("RunService")

RunService.RenderStepped:Connect(function(step)
	fps += 1
	spawn(function()
		wait(1)
		fps -= 1
	end)
end)

and for the mobile detection: (if this is false it’s either PC or Xbox)