I would think that the fan is working since it cools the first floor just fine so let's go on that assumption. AC units don't "suck air" up to the second floor of a house. There are usually a set of dampers that balance the air flow between the ground floor and the second floor. Since you say the first floor is working fine I would assume you have a damper problem. Remember heat rises so the upstairs is going to be much hotter than the downstairs unless there is a proportional amount of air put up there. It might be that the people who owned the house before you closed the dampers upstairs to save money or a host of other reasons. As far as sucking in air from outside, that's a damper issue too. However, you've got a swamp cooler. They work by evaporative cooling so they trade off energy savings for increased humidity. Since the humidity outside is bound to be higher, this might be the way the system is designed. 
I wouldn't be concerned with the rotation of the fan since it seems to cool the first floor just fine. Typically, when running any AC system, you would want all the windows closed. Opening the windows is just going to bring in humid hot air that your swamp cooler will have to remove. Swamp coolers are typically very loud. Remember, you're trading off energy savings from not having a compressor with evaporative cooling that isn't nearly as efficient so it just stands to reason you'd need more of it to do the same job.
The best advice I could give you is to hire an HVAC contractor and have him look over the system to make sure it's running as designed. You can check the intake filter but other than that, this isn't a homeowner do it yourself project.
Hope that helps,

Dan