1) How much overlap is there between UV-VIS/FTIR Spectroscopy and Inductively Coupled Plasma Atomic Emission/Absorption Spectroscopy? Would someone who is fairly familiar with the former have much difficulty in successfully working with the latter?
To answer the first question: practically none. ICP-AES is purely a analytical technique. The fact that it is spectral information is coincidental. UV-Vis has analytical applications, but it is measuring something completely different.
To answer the second: the techniques are very different. ICP-AES is far more demanding in the area of sample preparation and method development. That's not to say you can't learn it, but being an expert in UV-Vis won't automatically make you an expert in ICP-AES, if that's what you're asking.
2) How much overlap is there between the analytical techniques of these different instruments? UV-VIS relies heavily on the Beer-Lambert Law. Is it similarly straightforward to perform analysis for ICP-AES and AAS by comparison?
First, ICP-AES is an emission (fluorescence) technique, so Beer's Law is irrelevant practically by default. The sample type is also completely different. Concentrations are determined using elemental standards. A better comparison would be spectrofluorimetry, but the techniques are so different in what they measure and how they operate that even here the comparison is a poor one.
EDIT: Didn't notice your mention of AAS on first pass. AAS is an absorption technique and here Beer's Law is relevant. So I suppose you could say there are some similarities between UV-Vis and AAS, but again I stress that these techniques are used to determine very different things. AAS is also kind of a dying technology; I hesitate to call it a waste of time to learn it, but ICP-AES, or better: ICP-MS, would be probably a better investment of your energy if you are interested in this kind of thing.