In the attached picture if you zoom in, there is a very slight blur on this mans freckles. It is still in focus, but it almost looks as if the picture was painted. How was that effect achieved?
Freckles aren't always sharply defined. It may be that that's just how the model looks. There's a fair bit of noise in the photo, and that may be contributing to the "effect" you see; I don't get the impression that it's painted at all, it just looks like a noisy photo to me. JPEG compression may play a role here as well.
If this is a Photoshop effect, what effect is it?
There's not enough information to know how this image may or may not have been filtered.
What type of lens was most likely used?
Looks to me like a fairly "normal" lens, i.e. something in the 30-70mm range, depending on the camera sensor size. There's not a lot of obvious distortion. There is, however, plenty of bokeh (blurring) in the background, which suggests a lens with a relatively large aperture.
The background is very blurred and the subject is very close up. What settings and/or lens would be best for that?
You want a large aperture and a large difference between the camera-to-subject and camera-to-background distances. You could probably take a shot like this with a 50mm lens at f/2 or f/2.8, with the camera fairly close to the subject and plenty of space between the subject and the background.
Despite it being from a phone, any suggestions from experience on what could possibly cause the grainy effect? Or how low the aperture is in numbers?
Smartphone cameras like those found in an iPhone usually have a fixed aperture around f/2. The grainy effect may be due to compression, or there may not have been a lot of available light, causing the phone to adjust sensitivity upward and resulting in a noisy image.