0. You're probably as good without it, unless you have a quantitative measure of what you're trying to do! What kinds of potentially offending sources are you looking at? What does your system look like, is it a PCB in space, does it have cables coming off it, does it have a metal enclosure, etc.? How quiet does it need to be? And how noisy is it, by itself? (Filters are reciprocal, hence used for filtering emissions from a noisy interior, just as well as filtering external noise for a quiet interior.)
1. Perhaps. Side effects are same as stacking caps in parallel for bypassing: there are resonances between components, because components aren't just a resistance varying with frequency, they have positive and negative reactance and thus resonate with each other at frequencies intermediate to their respective SRFs.
2. Yes, for the same reason that putting two caps in parallel halves their impedance. Given the same provisos as above -- namely, as soon as symmetry is broken (are they really in series or parallel, and nothing else? Really?), you'll get different answers.
The attenuation might not increase much though. If the source impedance is 200 ohms say (a typical cable-in-free-space hand-waving value), you won't accomplish much with a short stack of say 30 ohm ferrite beads, or even all that much from a tall stack of them (or many turns, when needed at lower frequencies). If you need 20dB of attenuation, that implies a CMC of 2kohm, which is quite a lot of ferrite beads in series.
For high impedances, the most likely offender to cause that symmetry breaking, is stray capacitance to ground, or other nodes, or free space itself. The equivalent circuit becomes a ladder network with alternating series ferrite beads and parallel capacitors. The capacitors don't have much impedance (you might have <1pF/bead for an average bead-on-lead sized part), but they add up, and a long chain of them has a large effect at high frequencies.
(In the same way, capacitors are only "in parallel" when the connections between them have an impedance significantly lower than the components themselves. If the strays cannot be ignored, you're going to end up with something different. For example, a chain of capacitors in parallel, with stray L between caps comparable to their individual ESL, makes a lumped-equivalent dispersive transmission line; its impedance is somewhat higher, and its cutoff much softer, than the ideal version that might've been expected.)
Regarding #1, it is effective to put inductors in series when the parasitic capacitance from the first component, resonates with the next component's inductance, and that resonance is well damped so that there is a minimal dip in the series impedance. By chaining components geometrically, a high impedance can be maintained over many decades of frequency.
This is a good way to construct bias tees for wideband RF work -- the filter has an approximately constant resistance, giving some minor, but consistent, absorption and reflectance (mismatch) over the passband. Impedances can be kind of arbitrarily high, though you'll have a hard time finding, say, inductors with a peak impedance of 100kohm+ at very high frequencies.
You certainly cannot null it (infinite impedance), not without an active circuit -- and in that case you're adding an external power requirement, noise, limited dynamic range, distortion and so on; it's no longer just a passive filter network.
This is a very general approach, but it works just the same for specific filters, like we use for EMI.
Anyway, back to EMI filtering: there's at least two wires coming in, and they're carrying DC power. So, there's at least as many modes we might be concerned with.
When the 2+ lines are carrying the noise in phase, and the DC currents are balanced (equal and opposite), you can use a current-compensated choke (aka CM choke). This mode is often the bigger offender, being more pernicious, harder to track down.
A CMC adds an arbitrary impedance in series, causing attenuation relative to circuit/system impedances. This is the CMC's rated impedance, or when rated as attenuation, that impedance as a divider into a 50 ohm analyzer. But you can't get CMCs with infinite impedance, so you can only get modest attenuation this way, and only over limited frequency ranges (the impedance inevitably peaks, falling off at higher and lower frequencies).
To do any better, you must consider the system as a whole, and provide some means to shunt the excess CM current, dividing it down arbitrarily far. This is where shielding and Y-caps come into use. (They only need to be Y1/Y2 rated, when mains voltage is in use; for an SELV adapter, these are not required, and I'm abusing 'Y' merely to refer to function.)
Meanwhile, differential filtering can be done at any time, with a ladder network. An ideal balanced filter isn't needed, with a large enough CM filter; so a normal-mode filter is most often seen. That is, one side is solid ground, and we use a basic ladder network to filter the power line. We can also afford quite large values (10, 100, 1000uF..), and indeed we need low filter impedances to satisfy circuit requirements (e.g. step load response, hot plugging, etc.).
This is why you need to know your system requirements from #0 -- how much of each, and what topology, is contingent on what frequencies and attenuations are required.
Finally, you must not overlook the whole system. If this is a standalone box on the end of a cable, pffbt, who cares, stick some caps on the leads and go with it. No cables, self contained battery, even more trivial. If it has other cables coming out of it, you can filter one as much as you like, but you still have total liability from the others. Maybe the other cables will be quiet and well-behaved, maybe they'll be connected to other assumed-hostile equipment, or maybe they'll be laid in harnesses or trays with exceptionally noisy sources (like switching relay contacts).
Tim