1.Stats: Should Claydol get a stat boost, Evolution, Mega Evolution or nothing?
Claydol is.. interesting to say the least. It is one of the earliest OU Pokémon that was even in-game designed for sake of competitive gameplay. After, it was blessed with a rather weak type combination, that was strong offensively, but weak defensively, which is Claydol's forte. It was successful enough to justify a counterpart in the next generation, Bronzor, which served alongside Chimecho and Mr. Mime as that region's early Psychic-type.
However, Claydol became useless quite fast. Its main purposes were dual screens and Rapid Spin, and the latter became irrelevant due to abundance of Ghost-types in DPPt and later with Defog buff in Gen V, and the former became just irrelevant because of the overall power creep and decline of conventional stall as a popular strategy. This decline has finally hit in the official games, as Claydol is no longer useful enough for Battle facilities, being one of the few Pokémon that sucks hard enough to not to be in a NPC team in Sun and Moon's Battle Tree.
So, what shall we do then?
Well, let's look at a potential evolution. Claydol has a massive 200 BST gap from its pre-evo, Baltoy, which makes it more fitting for a mid-evo than a true evolution. However, if it were to gain one, it would be either far slower than Claydol(Claydol has decent speed for a wall) or be like Scizor and Porygon-Z and have a completely different stat distribution from its pre-evolution, one more geared towards offense.
A stat boost is also unlikely, because of the large gap and its status as a counterpart to Bronzong, which has also quickly declined from top tier OU to barely usable in OU. If it were to happen, however, it is hard to say which stat needs it most, because it is fairly balanced already.
A Mega Evolution would not work. Mega Aggron, Steelix and Audino all show defensive Megas do not work, unless they are like Mega Sableye and can be immune to status. Since Claydol would likely retain Levitate, there would be no point in it. An offensive Mega would be very cool, but it would be severely outclassed, again, as Mega Blastoise shows.
2.Should Claydol get more abilities?
Yes. While Levitate would make most Pokémon forget this idea, in Claydol's case it has a counterpart that has abilities other than Levitate, Bronzong. Aftermath, Telepathy, Magician, Sniper, Super Luck, Telepathy and Wonder Skin and Synchronize, Trace, Sand Rush, Sand Force, Sand Stream, Sand Veil are all valid abilities for Claydol.
Outside of this Magic Bounce would be fantastic.
3. Should Claydol get more moves?
Yes. The most obvious missing move for Claydol is Recover, but outside of that Energy Ball, Flash Cannon, Iron Defense, Hex, Stored Power, Refresh, Miracle Eye, Mean Look and Meditate can be given to Claydol.
Head-based moves like Iron Head, Head Smash would be cool as well.
Thunderbolt, Thunder and Blizzard can also be granted. So can Aurora Beam. Moonblast would be cool as well.
4.What additional typing Claydol can have?
Rock is the most obvious one. After that comes Normal. Debatably there is also Grass.