Is your phone charger on all the time? If so, it will drain your battery over a couple day period. You want to connect it to a supply that is only live when the ignition is on.
When you disconnected the battery did you disconnect the negative wire at the battery terminal or at the frame. The proper place is at the terminal. Then there is no way you could get a spark off the positive terminal if the negative terminal is not connected. If you got a spark with the negative disconnected at the battery there may be something else going on with your electrical system.
You need the battery indicator bulb working to get the alternator to excite. It is possible to have the alternator self-excite with residual magnetism in the rotor, but you need to revthe engine to more than 2500 rpm, possibly as high as 4000 rpm.
How old is your battery? Your problems seem to indicate that it may be a bit past it's prime, especially with the recent charging issue, and it would be a good idea to replace it before going on such a long trip. If it has sat for a week or two with no charge on it, there is the danger that it has lost a significant portion of it's storage capacity. Batteries do not like to sit with less than a full charge.