(1) Measure the impedance.
Make measurements at as many frequencies as needed for the application (including the maximum harmonics of signal frequencies), sampled as often as needed to get a "smooth" sampling of the function \$Z(F)\$.
An ideal two-terminal component, like an RLC, is a one-port, so this is a simple enough measurement, using a reflectance bridge for example, and as a passive (non amplifying) element, the impedance will be strictly positive-real. If the impedance differs widely from \$Z_0\$ (typically a 50Ω system is used, e.g. commercially available VNAs) in certain ranges, matching networks or other methods may be required to get adequate precision.
Apply the Padé approximant, obtaining a rational polynomial that best-fits the sampled data over the range desired. Increasing the order improves accuracy, to a point, beyond which additional fitting accentuates noise (errors in the measurements) and worsens interpolated and extrapolated results (adding a stipulation for some resistance at minimum and maximum frequencies may be helpful in this respect, at least to keep it from being too badly behaved).
This is essentially done, down to isomorphism, or to say the "solution is left as an exercise for the student". An RLC lumped-element circuit corresponds to a polynomial, and vice versa, give or take some flexibility in both spaces (for example, you can choose a parallel array of series RLC elements; or a series array of parallel RLC elements; or a ladder network; or etc.; the polynomial can be expressed as a straight rational, or factorized, or a continued fraction, etc.).
I'm not aware offhand of an algorithm to solve for a schematic based on an impedance plot, or polynomial, but that's not to say one cannot exist (clearly, a solution is possible, given the above; you might just not be able to enumerate every possible circuit (or class of circuit, given possible infinities) that fits the function).
(2) There is no general answer here, because:
a. Component parasitics are defined by component construction (length, aspect ratio, geometry, materials..) and cannot be changed in-circuit.
b. Where series or parallel combinations are acceptable, one or another impedance can be made to dominate over some frequency range, but they can only share when their impedances are proportionate (which in practice, means identical or very similar components/types). Maybe this doesn't matter for a strict impedance analysis, but it matters to practical circuits where the current or voltage distribution between components implies power dissipation in them, and a given component is limited to some maximum ratings in all three variables (V, I and their averaged product P).
For example, in a power converter, it might be that a parallel combination of ceramic and electrolytic is used, where the total ripple current exceeds the rating of each component type, and they need to be chosen (value, ESR, and number in parallel; and to some extent, stray inductance between them) such that RMS current ratings of both are respected. Too much of one or the other type would cause current to dominate in that type, and thus approach its limiting rating.
You will also encounter situations where the assumptions in (1) fail, e.g. the component ceases to behave as a 1-port, it has common-mode impedance to its surroundings. For example, you can't run 1GHz through a 50Ω 100W ceramic power resistor in any meaningful way: its body length is multiple wavelengths and will radiate to its surroundings. Even within a shielded enclosure, the impedance matching effects of those reactances will be visible, at each terminal with respect to that reference plane (shield).
You will also encounter cases where the RLC equivalent is simply a poor fit. Transmission lines are such a case (a one-port of which might be a TL stub, so we don't have to worry about the (2-port) transfer function yet). These give a rough fit by placing an RLC at each resonant frequency (i.e. harmonics), but a perfect fit requires as many LC elements as determined by the electrical length and desired bandwidth (which grows quadratically in their... product, I think it is?). These are cases where a one-dimensional approximation may be desirable: i.e. RLC circuits plus transmission lines, but the overall network still being analyzed as a point-like circuit (or infinite speed of light, but for the TL elements themselves).
As for references, I have regrettably few to offer; more generally, you may find insight from analytical network theory. Which can go all the way back to Zobel's (and others) early work on filters, e.g. https://archive.org/details/bstj2-1-1 , up to Zverev and others. Practical matters, like series-parallel connections of components in applications like power converters, may be found in books on such topics.
