First, this is my current understanding of things, using the Universe Sandbox.
To have the same surface gravity as Earth's on another planet that's smaller than Earth, you would have to increase the density of the smaller planet.
For example, if you would keep the density at Earth's current 5.51 g/cm³, Planet B with 0.5 of Earth radius would have 0.125 of Earth mass and only 0.5 of Earth surface gravity. To get to the surface gravity up to normal Earth, you would have to double the mass to 0.25 of Earth, which would mean a density of about 11 g/cm³ for Planet B. Now, as far as I understand, that density would not really be possible, even with a very heavy core, like pure iron. Fictional materials aside, a Planet B with 0.5 of Earth radius and same surface gravity cannot exist. I think I'm pretty safe so far.
Now let's assume a Planet C with 0.8 of Earth's radius. If my calculations in Universe Sandbox are correct, then that planet would have about the same surface gravity as Earth when its mass is about 0.644 of Earth which would mean a density of about 6.93 g/cm³. I think that would be plausible.
Now, to my actual questions:
Q1: Assume Planet C with 0.8 of Earth's radius and 1 Earth surface gravity which would be achieved by a higher percentage of Iron (I really have no idea about planet compositions, I just read somewhere that more iron would be one way to increase density). What would the weather be like on that planet? Especially regarding storms, would they be more/less frequent or more/less intense?
Q2: Assume the same Planet C as in Q1, except the land masses are more like in this rough image: Map as a rotating Globe: https://drive.google.com/file/d/1yCxESjBvE53VRc_qQPJHISGH2ZS1d3bP/view?usp=sharing
What would the weather be like on that planet? Especially regarding storms, would they be more/less frequent or more/less intense?
Q3: Assume the same Planet C as in Q2. Which variables would have to change for more frequent and more intense storms. For reasons I won't get into here, the 0.8 Earth radius is fixed, so I guess the only actually variable variables here could be the Planet's density and the core materials. If someone of you really knows their stuff, perhaps other variables could be the distance to the Sun or intensity of the Sun, but that's where I have virtually no knowledge in and I would be hesitant to change those things in my setting.
One more thing I should probably clarify: Apart from Storms, the average temperature and atmosphere should stay similar to Earth, or at least habitable.