I agree with the existing answer that feature scaling is a superset into which techniques like mean normalization, residual normalization, etc falls under.
So, assuming that by feature scaling, you mean the techniques other than mean normalization, I would attempt to answer your questions:
1) Can I mix and match these two approaches? e.g. Feature Scale x1 and
Mean Normalize x2?
In most cases No. Generally, only one normalization technique is used and it pretty much suffices the need. In addition to that argument, it should also be noted that any normalization technique introduces duplication in the data records (not necessarily redundant duplication).
So, pretty much a single normalization technique would suffice most of the times.
2) How do you determine which of these options to apply? It seems that
either could accomplish the task of increasing your convergence
rates... I suppose you just need to know your data set to understand
which will reliably reduce your values while leaving as few outliers
Yes, you are right. The selection of the technique depends on the data. And the feature scaling (and normalization) process comes under the process of data cleaning. So, it is done immediately after the selection of the relevant data for the analytics process.