Had to ask, wire colors are a bit confusing. Wire colors in Europe, United Kingdom and other places are different
So there are 6 wires coming out of the ceiling (red, black, ground x 2
That must be a typo.
switch is pigtailed to the red wires in the panel in the attic.
I assume that "pigtailed" as you are using the term, means connected. A pigtail is a short piece of wire that is added to a connection so that additional connections to a wire can be made.
I also assume that "panel" means the junction box. It helps to be consistent in the use of terms.
Not an admonishment, just information (I realize that you are probably not familiar with the jargon).
A wire is a single wire. A cable is two or more wires in an outer covering (sheathing). The use of the term "wire" to refer to both gets confusing.
To answer your question about the white wire being hot.
What you have is called a switch loop. The white wire is used to take power to the switch and the black wire is used to bring the power back to the fixture. It is done that way so that you have a black wire as hot in the fixture box. The white wire should be redesiginated as a hot by coloring both ends some color other than white or grey.
It is unusal to have all the outlets in a room split as you describe. Usually only one is split for use as a lamp outlet. The way that this has been done is also a bit unusual but perhaps there is a valid reason.
You may do away with the split outlets by replacing them and cap each end of the red wires with a wire nut. You could also make both halves hot all the time by connecting the red wires to the black wires in the junction box. Would probably be best to replace the outlets and marking the red wires "unused" or "dead" on both ends. Not required to do that but would be less confusing for the next person, or even yourself when you come back years from now.
You cannot take power the for the ceiling fan/light from the switch location as it is presently wired. There is no neutral at the switch.
You can run power, 2-wire cable, from the junction box to the ceiling box and then run 3-wire cable from the ceiling box to the switch location for a switch loop.
Or you can make the switch leg that presently runs from the junction box to the switch a power cable. Then you can use the two 2-wire cables to take hot and neutral to the ceiling box. It would have been neater to have used 3-wire cable but since you have already run the two cables you can use them. Connect the whites of those two cables to the white of the cable from the junction box. Connect the black of the wire from the junction box to each switch. Connect the black of the two new cables to the other side of the switches.
The junction box will have to be rewired. Connect all blacks together. Connect all whites together. Cap all red wires if you have not already done so.