What are the options to level out the air conditioner

I would consider a dehumidifier which will pull moisture out of the air. I'd also check into why the wall is getting moist. Are you sure there is enough insulation in the wall, because you definitely should not have moisture condensing on or in the walls.

An air conditioner will make the room colder which you probably don't want if the weather is already turning cold. The dehumidifier will pull the moisture out of the air without cooling the air the way an air conditioner would.

For the time being the dehumidifier should pull moisture out of the room for you. The specs for the appliances (dehumidifier or air conditioner) are usually fairly accurate, most notably on larger name brands. I've found knock-off and smaller brands to be a bit sketchy when it comes to performance, so I've learned my lesson and usually go for the larger more established brand names when it comes to things like this.

I have never covered mine and this article also seems to recommend not covering it:

Your central air conditioning unit consists of a compressor and condensing unit placed outdoors in a metal housing. These units, built to resist the weather, generally do not need a cover. In fact, covers can cause problems because they trap moisture and create an inviting winter home for small animals.

Professionals who service the units tell me that most of the damage they see in spring was caused by rodents living in the units and chewing on wiring.

If your air conditioner is subject to falling ice or other debris, you could cover its top with a piece of plywood, plastic or metal held in place by a weight.
Reference: http://misterfix-it.com/blog/?page_id=36#cac

They make a great point that a cover would provide a perfect winter home for animals which would cause damage to your air conditioner.