Regarding item 1, what is GEZZ(U) ? As for speed, how much of the run time is prior to seeing the first solver output vs. while solver output is occurring? If you are not using Mosek and have access to it, try using it, because it is more reliable and numerically robust, and likely faster, especially on difficult problems, than SeDuMi or SDPT3. Try every SDP solver you have available. If you show the CVX and solver output, perhaps some of the more expert forum posters could determine something from seeing it. I think forum readers will need to know more about the numerical values in GEZZ(U) to determine whether there might be poor scaling, condition number, or otherwise which could be contributing to solution difficulty, and therefore to long solver run time. That said, CVX is not designed for speed, and in particular it is not designed to be fast in transforming model inputs for submission to the solver; rather, it is designed to save human model building (entry) time.

You need to be more specific regarding item 2. Can you show the smallest possible reproducible problem, complete with all input data, which exhibits the error, as well as showing all CVX and solver output, including the error messages?