The only way to resolve DOF noise is to use more AA samples. The actual number of pixel samples in Arnold is the square of that number, however, so don't go too crazy with it. (AA samples of 4 means 16 pixel samples, AA samples of 5 means 25 pixel samples, etc.) This is because doubling the sample setting will get you roughly half the amount of noise, which is intuitive. However, it will take four times as long.
You often can get away with reducing the other sample settings as you increase AA samples; e.g. AA samples of 1 and GI diffuse samples of 5 is roughly equivalent in indirect diffuse noise as having AA samples of 5 and GI diffuse samples of 1. Because you need to increase your AA samples to deal with DOF noise, you can probably decrease your other sample settings (lights, GI samples) to compensate so that your render time doesn't go up a lot.
Also for DPI, Arnold knows nothing about it. If you want a 300 DPI image in the same size, you need to render out of Arnold at a higher resolution so that you have enough pixel data. For example, if you had 1920x1080 image, at 72 DPI that would fit an area of 26.67 in by 15 in (1920/72 by 1080/72). But if output that same image at 300 DPI, it would only take 6.4 in by 3.6 in (1920/300 by 1080/300). So, if you needed an image at least 12 in wide and 16:9 ratio, you would need 12*300 = 3600 pixels wide and 3600*9/16 = 2025 pixels high.