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This inflates my clicks, can I filter those out?

Yes you can, create a new profile based on your original profile and name it something like 'domain - clean'. For each different outbound clicks or download prefix you have, create an exclude filter. You do this by:

1. choosing a name for the filter, something like 'Exclude Downloads';
2. selecting 'Custom filter' from the dropdown;
3. selecting 'Exclude';
4. selecting 'Request URI' in the Filter Field dropdown;
5. setting the Filter Pattern to '/downloads/(.*)$' for a prefix '/downloads/';
6. setting case sensitive to 'No'.

For some more info, see the screenshot under Screenshots.

Can I run this plugin together with another Google Analytics plugin?

No. You can not. It will break tracking.

How do I check the image search stats and keywords after installing this plugin?

Check out this tutorial on checking your image search stats and keywords.

How do I check my outbound link and download stats?

Check out this tutorial on checking your outbound click stats.

I want the image search keywords in one big overview...

Create a Google Analytics filter for image search.