Considerations for using various AC->DC adapters of different voltages
First of all, before answering your questions, it is important that you understand the difference between  regulated and unregulated supplies.  Regulated supplies will put out close to their rated voltage regardless of the load.  Unregulated supplies will put out a much higher voltage with no load or a small load, and only approach their rated voltage under the amperage specified on the device.

If you are powering just a few ICs, then the current drawn will be negligible  and an unregulated supply will be supplying a much higher voltage that you expect.

USB power supplies will most certainly be regulated, and close to 5v (the spec calls for 4.75v to 5.25v).  Most cell phone chargers will also be regulated, but don't count on it.  As you get higher up in voltage, you will find that less and less supplies will be regulated.

Before connecting any of your supplies to a circuit, check the voltage with a multimeter.

Can I mix them in ways that circuit analysis says (e.g. parallel, series, series opposed)


Not a good idea; these are not the same as batteries.  In particular, NEVER put two power supplies in parallel.  You may or may not get by putting them in series, it depends if the ground wire of the supplies is actually connected to the ground in the outlet (most are not).

So it may be possible to get a negative supply voltage by connecting the + lead of one power supply to the ground of the other, such the that ground of the bottom supply will be negative, the + of the top supply will be positive, and the ground of the top supply (connected to the + of the bottom one) will be a ground reference for both of them.
Once again, check your voltages with a meter before connecting anything to a circuit.



What is the role of the specified current in the power supply, is it
the max current or the current that it provides at all times when connected.


It is just the maximum current.  Power supplies don't push current into a circuit, rather a circuit draws what it needs.

If two power supplies output the same voltage but their currents are
distinct what would that indicate?


Only that they can supply different amounts of current to a circuit.  Once again, do NOT put two supplies in parallel.