You're the photographer; if you're happy with them, then you did them right. The beauty of art is that there is no 'right' or 'wrong'. Could they be improved? Yes, I think so. #1 is suffering from over-exposure in the petals of the flower; the white is over-exposed to the point of being "blown" or pure white without detail. Reducing your exposure by a stop or so, would have allowed for some of that detail to be preserved. I suspect your camera's meter was fooled by the bright area surrounded by dark. Consider reading your manual's section on 'metering modes' with special attention to spot and centre-weighted modes.
Both mushroom images suffer from the same issue, 'though the second is somewhat more pronounced. Lenses, especially consumer 'kit' lenses don't like to be pointed toward the sun. This has caused the excessive purple in the background and the general hazy appearance. Moving around 30 or 40 degrees would have elminated this and resulted in sharp, clear images.
On the second one, you have a lot of 'stuff' on the sides that doesn't contribute anything. A 'portrait' position for the camera would help focus attention on the mushrooms.
Directly in back of the target, there are some bright distracting flowers. This is like taking a picture of a person and having a light pole come out of their head in the background. It breaks concentration and hurts the scene.
(he could turn the iPhone on its side and move a bit)
I change lenses and exposure on my iPhone all the time. I can't think of a camera app out there that does not give some form of exposure control. I also have lenses from moment.co that are top quality lenses with multiple glass elements.
1) I would have touched the screen over the white of the flower to try and get that with a good exposure and just let the background go dark. Also, there is one other small flower in the shot and I feel that unbalances it a bit, either do it without the second or find a third flower to include.
2) The mushrooms are just fighting with too much other junk. I would have pulled the dead leaf running through the mushrooms (like lifting a twig on a golf green).
3) Like the previous shot; the subject is right in the center and there are some distracting items (like the blades of grass in front of the subject that need a trimming). The backlighting is sometimes fashionable, but I would also look to get the shot with the light coming in from the side. Also, try using your hat or other object held out with your other hand to control the light (and close-up shots often need more light on the subject so might add a simple reflector to bounce some light in there).
I have great photos taken with my iPhone 6 Plus.
I also have 3 snap on "lenses" for macro, wide angle, 2x zoom and fish-eye (one of the lenses turns around for the fish-eye effect).
You have the sensor, then the lens, and then you put a piece of glass in front of the lens.
Obviously you can take good pics with the phone, but you can't control almost anything.
On the iPhone you can control the shutter speed up to 0.5s, the white balance, ISO and the focus.
You can't control the apperture, ISO performance, image quality is not very good, dynamic range also...
Conclusion, a good photo can be taken with a phone, but you will always get a better photo with a dedicated camera