Ethereum's Proof-of-Work mining algorithm is designed to be ASIC-resistant. Basically this means that using an ASIC should not be beneficial enough to warrant the high cost of ASICs. So
Yes, at least in theoryan ASIC gives you a lot of hashing power, but it costs a lot. So the miningquestion you need to ask yourself (and possibly research) is most profitable with regular graphics cardswhether the high cost of an ASIC can be compensated by its sheer hashing power. For coins such as Bitcoin the domination of ASICs is obvious, but not so much for Ethereum.
There have been stories aboutare various companies building an Ethereum ASICASICs around but I haven't seen much evidence that it would be beneficial enough.
So, as for the answers:
They both use the same mining algorithm currently. If you want a lot of hashing power easily, sothen buying an ASIC is maybe an ok choice. If you are simply looking for quick profit, noASIC may not be the best option.
I'm not very up-to-date withAs The Renaissance corrected me, ETC but I doubt they will be changing thehas plans to maybe change its algorithm completely. They may make some minor adjustments to it but the basic idea will probably stay the same, so the answerBut nothing is also nocertain yet.
ETH's mining algorithm will not change. ETH will transition to a Proof-of-Stake model within (hopefully) the next few years and at that point there is no mining at all. In any case ETC's events do not directly affect ETH.