Yes, all of those symptoms could be related to gluten, however, they might not be directly related, but rather indirectly related. It is possible that over the years gluten has done damage that might not be undone very easily.
For example the heart burn. It may go away immediately on a total gluten-free diet, or it may not. If you have developed further complications, for example, scar tissue formation. I think it is controversial anyway whether reflux is associated with celiac/GS. I believe it is, but some studies have found that it is not. However, personally I don't trust a lot of the studies because of the criteria they use. Celiacs positively diagnosed with biopsy where "healthy" controls in my opinion may not be healthy at all if they have a hidden gluten condition.
I have a lot of the same symptoms that you do. For me, going even partly gluten free "cured" about 90% of my anxiety and depression. But it did nothing for my rashes and my numbness and tingling in the hands and feet. The doctor says it will take months of being scrupulously gluten free before I will see improvement in most of my symptoms.
In my example, the hands and feet tingling is peripheral nerve damage that has been occurring for more than 20 years. I don't know how long it will take my nerves to repair themselves, if ever. The theory is that celiac gut damage prevented me from absorbing vitamins that are necessary for normal repair of cells, in my case nerve sheath cells, but also cells in every area of your body. If you have had trouble absorbing fat, you could be deficient in the fat soluble vitamins, which can be the direct cause of your symptoms. So removing gluten is key to healing the gut. But the rate at which your symptoms will improve might have more to do with how well you are able to get caught up with your nutrition. This is not always straightforward. For my example again, the gluten problem has caused me to also be sensitive to milk, and milk is where I had been getting all my vitamin D. Now that I am going to give up all dairy as well as gluten, I need to pay attention to getting enough vitamin D as well as calcium and magnesium, and vitamin A and K and zinc, and so forth.
So the answer is that yes going gluten free is the first step toward improving most if not all your symptoms, but if you do not have improvement in some of them, you may need to research a little into specific deficiencies and long term damage that may require some extra attention.