If I understood well there are two questions here, mainly.
Is it possible to play a sound on two or more audio output devices simultaneously, and how to achieve this?
Is it possible to loop back data through a audio input (recording) device so that is is played on the respective monitor i.e for example sent through the audio stream of Skype to your partner, in your respective case.
Answer to 1: This is absolutely feasable, all independent audio outputs of your system can play sounds simultaneously. For example some professional audio interfaces (for music production) have 8, 16, 64 independent outputs of which all can be played sound simultaneously. That means that each output device maintains its own buffer that it consumes independently (apart from concurrency on eventual shared memory to feed the buffer).
How?
Most audio frameworks / systems provide functions to get a "device handle" which will need you to pass a callback for feeding the buffer with samples (so does Open AL for example). This will be called independently and asynchroneously by the framework / system (ultimately the audio device driver(s)). Since this all works asynchroneously you dont necessarily need multi-threading here. All you need to do in principle is maintaining two (or more) audio output device handles, each with a seperate buffer consuming callback, to feed the two (or more) seperate devices.
Note You can also play several sounds on one single device. Most devices / systems allow this kind of "resources sharing". Actually, that is one purpose for which sound cards are actually made for. To mix together all the sounds produced by the various programs (and hence take off that heavy burden from the CPU). When you use one (physical) device to play several sounds, the concept is the same as with multiple device. For each sound you get a logical device handle. Only that those handle refers to several "channels" of one physical device.
What should you use?
Open AL seems a little like using heavy artillery for this simple task I would say (since you dont want that much portability, and probably dont plan to implement your own codec and effects ;) )
I would recommend you to use Qt here. It is highly portable (Win/Mac/Linux) and it has a very handy class that will do the job for you: http://qt-project.org/doc/qt-5.0/qtmultimedia/qaudiooutput.html
Check the example in the documentation to see how to play a WAV file, with a couple of lines of code. To play several WAV files simultaneously you simply have to open several QAudioOutput (basically put the code from the example in a function and call it as often as you want). Note that you have to close / stop the QAudioOutput in order for the sound to stop playing.
Answer to 2: What you want to do is called a loopback. Only a very limited number of sound cards i.e audio devices provide a so called loopback input device, which would permit for recording what is currently output by the main output mix of the soundcard for example. However, even this kind of device provided, it will not permit you to loop back anything into the microphone input device. The microphone input device only takes data from the microphone D/A converter. This is deep in the H/W, you can not mix in anything on your level there.
This said, it will be very very hard (IMHO practicably impossible) to have Skype send your sound with a standard setup to your conversation partner. Only thing I can think of would be having an audio device with loopback capabilities (or simply have a physical cable connection a possible monitor line out to any recording line in), and have then Skype set up to use this looped back device as an input. However, Skype will not pick up from your microphone anymore, hence, you wont have a conversation ;)
Note: When saying "simultaneous" playback here, we are talking about synchronizing the playback of two sounds as concerned by real-time perception (in the range of 10-20ms). We are not looking at actual synchronization on a sample level, and the related clock jitter and phase shifting issues that come into play when sending sound onto two physical devices with two independent (free running) clocks. Thus, when the application demands in phase signal generation on independent devices, clock recovery mechanisms are necessary, which may be provided by the drivers or OS.
Note: Virtual audio device software such as Virtual Audio Cable will provide virtual devices to achieve loopback functionnality in Windows. Frameworks such as Jack Audio may achieve the same in UX environment.