2 GIPF descriptors can at most be used to empirically build prediction relationship. For example, you can collect a large set of known solubility data for organometallics and calculate various GIPF descriptors for them via Multiwfn, then try to correlate them by e.g. linear fitting and neutral network models. If the model looks good, then it can be used to predict solubility for other organometallics species.
If you need to accurately calculate solubility, it is quite difficult and time-consuming, see J. Chem. Theory Comput. 2021, 17, 3700−3709 for discussion

3 They are quite different. GIPF is simply a set of molecular descriptors based on molecular electrostatic potential over molecular surface, if you read some introductory materials about COSMO-RS (e.g. DOI: 10.1002/wcms.56), you will find there is no direct comparability between COSMO-RS and GIPF.

2/Other than a G09 output file and the Multiwfn programme, what do I need to get the solubility value?

3/Is there a similarity between GIPF and COSMO-RS?

Is it possible for GIPF descriptors to determine the solubility of a system  containing metal atoms, such as Cu atom?
Thank you very much.