1. Is Lightening Network only out to solve BTC problems? If no, are all altcoins eligible to use it, if not now maybe in the future when the need arises. Or would there be or is there solution to altcoins limitations?
Altcoins are welcome to try to copy Lightning Network's design, if they have the features necessary for them, it could work.
2. Can the LN be used as a store of value? Which means that I can transfer some amount of btc there and leave it for a long time for saving purposes? If yes, any security risk?
The funds will stay on Lightning Network for as long as the channel will be open. But you can't control the node that you open your channel with, so you can't rely on your coins being on LN for years. When the channel closes, your funds will become available on mainnet.
3. Can a user add someones wallet address to the network without his knowledge? What I meant is that must the sender and receiver be authenticated before transaction?
Lightning network doesn't have addresses, it has payment requests that are generated for each new payment.
4. Since the blockchain only records transaction at opening and closing a channel, will it be nice to have a mechanism that mirrors the transaction in the LN to the blockchain for on blockchain record keeping and security even when they are not charged transactions fees?
Lightning network transactions are signed on-chain transactions that don't get broadcasted. The act of closing the channel is actually broadcasting the last state, so the security of LN transaction is very similar to onchain. The possibility of fraud comes from broadcasting a previous state, but there are mechanisms to combat that.
6. The increase in the adoption of LN will invariably reduce the reward of the miners, Will this not amount to further increase in the on blockchain transaction fees?
It's not guaranteed to reduce transaction fees on chain. People will still be doing onchain transactions. And miners don't control transaction fees in any way, they are decided by the fee market.
8. In the case of buying coffee. If I have to buy coffee from 5 different stores, do I need to open and close channel 5 different times? Isn't the cost of opening and closing these channels equal transaction fee on the blockchain?
All you need is an open channel that can find a route to all these stores. If the whole network will be fully connected without isolated "islands", you won't have to worry about it.