Electronics are perhaps unique in terms of electrical devices in that they are usually quite sensitive to differing voltages and currents. In practical terms, the reason for that is that modern electronics are generally made to be as small as possible to pack as many features into as small as possible a space.
If we assume that by 'electronics' you mean 'integrated circuits', then certainly you'd need to be able to generate power at precise voltages and currents (and probably only Direct Current, not Alternating Current) so as not to potentially damage your equipment.
That said, your novices can always practice on electric kettles and toasters first. Generally speaking, electrical items that deliberately generate heat can handle much higher levels of current so would be a great place to start. If you blow them up, then you shouldn't be trying to charge a mobile phone.
Perhaps the best testing device for novices would be fans. Get them to practice spinning the blades of a fan at a very precise speed (by applying a specific voltage and current through them) and when the novice can control the blades of a fan consistently and for an extended period, then they have sufficient control to start on electronics.
Now for the direct contact part of the question; Wireless Power Transmission has been around since the days of Nicola Tesla, who first experimented with this. Right now, there are induction plates that allow you to charge any mobile phone battery just by placing the phone on the plate - no cable required. The linked article shows the two different types of wireless power transmission currently understood by science and gives some insight into their practical application.
Why is the science important? Because your magicians don't have to resort to magic to induce power in a remote object. Ultimately which options are available to them will depend on how they use magic to generate power, but working with the edit that they can only generate an electrical current directly from their skin, then the same technique that induction plates use could be employed by your magicians to charge mobile phones. Touch would not be required, but close proximity would.
Many of the questions you ask above are related insofar as whether or not cables are needed is the same as whether or not touch is needed; given induction plates the answer is clearly no, so the rest of the question comes down to control of the power source by the magician him or herself. Whether or not magic can generate power with that level of precision, I leave to you.