I will be using only one of the features you mentioned, Manipulating Matter, or as you mentioned supply/retract energy.
First of all, we have to have something very clear. You can give energy and you can remove it, but it doesn't cease to exist, it has to be moved to/from somewhere
Secondly we have to be aware that everything we currently know is composed out of molecules and atoms, which in turn are essentially a form of matter composed by energy.
Thirdly, knowing everything is made out of the same basic element, we can deduce that with the ability to move that element around, we can alter matter. And luckily for us, it is currently possibly and proven to be possible. There is even a catalog for it in the Periodic Table. Without going into too much detail, if an element has an atomic number of x, and another has an atomic number of y (and y>x) it means that the element is heavier and contains more energy (there's also the issue with stability, but that's going into too much detail)
1) Yes, you can turn Copper into Gold, Copper (Cu) has an atomic number of 29, while Gold (Au) has one of 79, They are even in the same column, meaning it's literally a matter of (no pun intended) adding matter, to create gold you would use atoms (at least 2) of Copper, to create a single atom of Gold and another atom (The remainder matter).
2) In theory yes, you could make atoms collide at a high speed and create explosions, however why would you need to put so much effort (You would be creating a nuclear explosion)? There are atoms which are unbalanced, meaning they are volatile, and prone to react with air in big bangs. Not as big as a nuclear explosion, however you could control it easier.
3) "Pure" Water is a mixture of 1 atom of oxygen (O) and 2 of hydrogen (H), H2O. Air on the other hand is made out of mostly Nitrogen, with some part Oxygen, Carbon Dioxide and other vestigial gases, interestingly enough, H20 is also in air, so, while you wouldn't be creating H20 molecules, you could use your powers to compress the H20 molecules in order to convert from Water Vapor into Water or even Ice.
4) Well Yes. It's funny if you think about it. Oxygen is highly flammable. So is Hydrogen in its natural state. However, together they balance each other and become stable. But if you split the molecule into Oxygen and Hydrogen (you would need to use an immense amount of energy) you could then have 2 very dangerous elements, which would only need a single spark to turn into fire. So, in a way, it is possible to set fire to the rain. Bonus points because you'd also make all impurenesses that the rain has dissolved fall as solid matter.
5) There are different types of lava. Lava is essentially heated Silicate Materials (Rock) with other types of matter in it. You already know how to create different molecules, so it would only require you to know the recipe. Turn something into Silica, charge it with energy and presto, instant Lava!
6) Once again yes, you would be able to create Graphene, as long as you can supply the matter and energy to create Graphene
Manipulating matter, going nuclear, moving electrons and nucleoses can either take or produce a lot of energy (depending if the materials are stable or not). With that said, you would need a strong source of energy so you could contain and use it to manipulate matter. Your limitation would pretty much be the same as Superman. Sun could potentially be your best power source, since you could as well alter your own structure in order to make yourself immortal (or rather, you can renew your cells as so you wouldn't be able to die from aging). You would lose the ability to do all of this the second you ran out of useable energy
You can Fly! In theory you could also move all molecules away from one area, creating a sort of 'void' space. This is important because the only reason why we aren't in perpetual motion is due to attrition (More attrition requires more force to keep in motion, less requires less force. Think about cars. On dry days you have more control because you can brake easily due to the tires being in contact with a rough surface, on an heavy rain day the tires will have poor contact and thus low attrition, making them slide), but if you have nothing to cause attrition you would be in perpetual motion (Null Acceleration, Existent Velocity). This is the same as flying without a power source.
You can also not breathe, because you can refresh your cells with oxygen without breathing.