First all there’s no such thing as a 3rd eye or chakra in qigong - these come from a different system so that seems confusing and that book might be a more modern mashup of other teachings - in the image above the word “gate” seems to be a translation into English for what most translations just call “points”.
Secondly you do not dissolve the points - these are important parts of your qi body, and basically represent the points where the meridians come close to the surface of the skin, making them easier to sense and work with.
What you dissolve are “blocks” - energetic knots of energy that interfere with the smooth flow of qi through the meridians. You also widen your meridians so they can carry more energy at once.
You do not have exercises in qigong that only focus on one point at the expense of the others, it’s considered important to clear all blockages in balance - i.e. evenly all over.
The acupuncture points (there’s several good ones in that area) are associated with the “Upper Dan Tian”, which is a storage center for qi. Developing the Upper Dan Tian allows psychic senses to develop as you cultivate more qi storage overall. The more qi you have the stronger you are.
Yes, exactly. And this is very safe, and even if you don’t complete the work you will still benefit form better health and longer life.
It doesn’t say facial gates - it says points in the brain. It’s very unlikely you will go there. You can find the facial points by consulting a good acupuncture book and using your fingers - the points are more tender than the skin next to them when you feel them.
You should see diagrams that label them based on the meridian they are on, and they have a number ore from 1 upwards for where they are on the meridian. There are several meridians in the head, and the Dan tians (there are 3) are all on the Dui-Mai meridian pair.
Like this: and the text should escribe to you exactly how to find it in terms of your finger-widths
I like the Root of Chinese Qiging by Jwing Ming Yang if you want a comprehensive reference work. There’s a list if qigong books worth consulting here:
Here’s an old post on cultivating qi though it’s a simplified explanation:
Well, not that book maybe - it seems distorted and dumbed down. 
It’s helpful to learn to cultivate qi and then run the microcosmic orbit to balance it with a teacher, but there’s a lot of helpful youtube tutorials that also talk you through it.