Does ASIC miner works in ETH and ETC

In order to determine if mining will be profitable for you or not, you should use a mining calculator. (You can just search for 'mining calculator' online.) The reason why is that profit will depend on how much you're spending on electricity and other factors. You will need to know the cost of electricity wherever you're running the ASIC. You'll need to know the hashpower of the ASIC too, from here the A10 Pro looks to be 500 MH/s.

You will also most likely want to join a mining pool (as opposed to solo mining). As this wasn't part of the question, I'm not going to spend time on it.

Now, let's move on to your specific questions.

Is it good to buy an ASIC Miner in Nov. 2020 for ETH and ETC mining ?

The first thing you'll need is a mining calculator to see if mining in your region can even yield any sort of profit. (You'll need to check for ETH and ETC - each one is different.) A quick look at the ASIC specs looks like it should be able to turn a profit. This isn't everything, though: you still need to buy the ASIC. It will most likely take some time to pay back. If this is 'worth it' for you is up to you, but this should help you make a decision.

You touch on two points that directly relate to this in your other two questions, but I'll answer each one separately. The above answer assumes that you'll have enough time on ETH and/or ETC to make as much as you'd like. The next two questions correctly question that assumption.

ETC mining algo change

ETC did have some proposals to make changes to its mining algo after being repeatedly 51% attacked with rented hashpower. If they change the hash being used in the mining algorithm, I would assume, but have not been able to confirm, that an Ethash ASIC would be unable to mine it efficiently. If someone can confirm this, I would be much obliged.

As of yet, no changes have been made, and their communications indicate this will not happen quicker than 5 months (6 in the article, 1 month has passed). Source

ETH mining algo

Ethereum plans on moving to proof-of-stake, which will most likely eliminate mining. (I seem to recall some talk of keeping some proof-of-work shards, but at the least, I wouldn't count on it.) While parts of this system are scheduled to be released in November of this year (2020), they do not eliminate mining and the proof-of-work chain. You can read about the Eth2 roadmap here. The phase of the roadmap that is supposed to transition mainnet to proof-of-stake is Phase 1.5, and is currently slated for a 2021 release, though this may be optimistic. This is something to consider when purchasing an ASIC, especially if the only two chains you are willing to mine are ETH and ETC.

Update: I forgot to address your question of profitability. This isn't really the forum for it, so I'll simply point out some basic facts, and urge you to do your own research. If ETC changes the hash in their mining algo, and we assume:

• That there are a non-trivial number of Ethash ASICs mining ETC right now, and
• ASICs made for ETH will not be able to mine ETC efficiently as a result

then there will be a bunch of 'freed' Ethash hashpower looking for something to mine. They will not necessarily turn to ETH, though. If they do, it would be a question if increased hashpower drives price. I don't have a qualified opinion on that.

An Ethash ASIC can be used to mine a multitude of other chains that use Ethash, so there options other than ETH and ETC. You may want to explore them.