color managment in fusion

While there is a Cineon Log [Log] tool....

a) you want to be working in linear in fusion, since that is how compositing tools expect to work with. You don't want to be converting to log or rec709 unless you absolutely have to.

b) the way you work in fusion is in linear but to see what you are doing you should be using viewer luts so you get preview in viewer of rec709 while processing is happening in linear.

c) You import any media and you use one of several tools to convert it to linear for working in fusion and than you bring it back to one unified deliverable in the end. Likely rec709 if that is your final destinaiton and no other work is done, or you bring it from linear to something for grading like DaVinciWideGamut/intermediate for color page grading or if you work in ACES than its ACES cg (linear) for fusion work and ACES ct (log) for color page grading and than when you are done with it all you convert to deliverable, such as rec709 or multiple deliverables.

Best to work in scene refereed color space rather than display refereed color space. In other words you work with large enough intermediate space which covers all the differnt cameras and assets and converts them to one big unified space where you can do grading and minimize loss of quality and data while keeping it visually consistent, and than you deliver in the end to something like rec709.

If you are using resolve color managed project settings than most of this happens behind the scene by resolve, although I prefer to go about it manually for more control, so here are some of the tools for fusion. in resolve you have CST, ACES etc.
d) tools for converting between formats in fusion are few.

ACESTransform [ATr] - A simple node that lets you perform color transforms using the ACES Input Device Transform and ACES Output Device Transform parameters.
OCIO CDL Transform [OCD] - Fusion supports the Open Color IO color management workflow by way of three OCIO nodes.

‚The OCIO CDL Transform node allows you to create, save, load, and apply a Color Decision List (CDL) grade.‚  ‚

The OCIO Color Space allows sophisticated color space conversions, based on an OCIO config file.

The OCIO File Transform allows you to load and apply a variety of Lookup tables (LUTs).
Generally, the OCIO color pipeline is composed from a set of color transformations defined by OCIO- specific config files, commonly named with a “.ocio” extension. These config files allow you to share color settings within or between facilities. The path to the config file to be used is normally specified by a user-created environment variable called “OCIO,” although some tools allow overriding this. If no other .ocio config files are located, the DefaultConfig file in Fusion’s LUTs directory is used.

For in-depth documentation of the format’s internals, please refer to the official pages on opencolorio.org.

Color Space Transform [CSt] - A simple node that lets you perform the kind of color transforms that LUTs do, but instead of using lookup tables, this plugin uses the same math used by Resolve Color Management (RCM) in order to do extremely clean color transforms without clipping.

Gamut [Gmt] - he Gamut node has controls to transform one color space to another and remove/add gamma curves. This node, along with the Cineon Log node, is primarily used to linearize incoming images and then reapply the applicable output gamma curve at the end of a node tree.

Cineon Log [Log] - The Cineon Log node is used to convert several different log camera formats to linear gamma and back again. Although the name implies that it should be used with Cineon files, it handles “log” gamma from many different digital cinema sources such as Blackmagic Design, Arri, and Red cameras.

There are all sorts of other tools for extra functions, influencing loading luts and use them, and most of all these I listed plus custom luts are available as viewer luts so you can work in one space, which is going to be most suitable for whatever you are doing and seeing it so that its not all washed out, too dark etc.

There is also a bunch of first and third party tools for conversions between color spaces, DCTL's and color adjustment tools. Channel shuffling, normalizing aux channels etc.