1) Who controls the white areas?
2) Are any of the forces noted on the same side of anything or do they all fight everyone else?
1. Based on previous maps, the white areas appear to be those that have not been contested and have remained nominally under government control.
2. This is more complicated because the enemy of my enemy is not necessarily my friend. The Islamic State, for example, is fighting the Syrian government and the US-backed Kurdish/Arab forces which means that although some of the US-supported Kurdish-Syrian forces have fought the Syrian government, they are primarily focused on defeating the Islamic State. It seems more like a circular firing squad. The US has tried to avoid supporting attacks on the Syrian government in order to focus on the Islamic State, but that has not always been possible. The Obama administration initially supported militias opposed to Assad, but could find few "moderate" Arabs to train and, since the Russian intervention, seems to have turned its focus on defeating the Islamic State exclusively. Trump seems to have followed suit.
The Russians are not shown on the map but they are important players. They are primarily fighting/bombing the Syrian militias focused on overthrowing Assad. That includes some Syrians the US has supported in the past, but apparently has cut off or reduced assistance. The Russians have been known to bomb Kurdisn/Syrian Arab forces by "mistake".
The Turks have a Syrian border area presence designed to prevent the Kurds from unifying its two areas of control. They occasionally bomb Kurds who enter this contested area. They pay lip service to opposition to the Islamic State and have fitfully called for the overthrow of Assad, but seem to concentrate their current attention on the Syrian Kurds who they claim are affiliated with the PKK Kurdish rebels in Turkey.
The Syrian government is fighting the Kurds/Arab forces supported by the US when they encounter them outside predominantly Kurdish areas. South of Raqqa we may see a full engagement between these two forces. Or, the Kurds may choose not to venture beyond their own territory and, not only avoid immediate war with Assad's forces, but cede the area south of Raqqa to the government. Raqqa is not a Kurdish region, so its disposition may result in a future conflict, or the Kurds may withdraw an leave it to the government. That remains to be seen.
Iran is sponsoring Hizbullah (Lebanese Palestinians opposed to Israel), and some of its own forces in support of the Syrian government. They are prepared to fight any group opposed to Assad.
As the Islamic State recedes, we could expect the Kurds and Sunni Arabs in alliance against the Iranian groups and the Assad government backed by the Russian air power. What will the US do then? Will we continue to back the Kurds and Sunni Arabs or will we let them face Assad and his allies alone?
This is the best I can do with what I have read. It is an oversimplification given the variety of groups in the fight. On the old forum I had a series of more detailed descriptions, but the situation is still fluid. Militias still continue to morph depending on the situation on the ground and tribal loyalties.
List of armed groups in the Syrian Civil Warhttps://en.wikipedia.org/wiki/List_of_armed_groups_in_the_Syrian_Civil_War