There is no limit on how many transactions it can handle, am I correct?
You are correct.
And is it right?
The only way to attack someone is to actually broadcast some old channel-state which is unfavourable for the attacked individual. This is perfectly possible but if that happens, the Multisigs and time-locks are set in a way that such transaction can be preferably spent by the attacked person before the time-lock elapses and thus moving every single satoshi into one's own wallet so that the attacker will lose all his money inside that channel
It is right.
The participants in a channel will share unbroadcast transactions. At any time, either participant can close the channel by signing and broadcasting the most recent shared transaction (which will result in both participants receiving their appropriate portion of the funds in the channel). The risk is that your channel partner might try and close the channel with an old expired transaction. However, the transactions that close channels are time-locked, so that your partner will not have access to those funds for a predetermined amount of time. During that time, if you can prove that there is a more recent transaction in the channel, then the time-locked transaction will allow you to take ALL of the funds from the channel immediately (before your channel partner's waiting period has expired). As such, your channel partner would be rather foolish to try and close the channel with an expired transaction unless he is VERY CERTAIN that you will not notice until the time lock expires.
The number of transactions depends on the number of opened channels and their capacity. There is a limit of maximum amount you can send, about 0.04 BTC.
Channels are currently being created with a limited amount of funds in them. This means that there is a limit to the amount that you can send PER CHANNEL. If you have multiple channels, then you can use them to send more funds. As Lightning Network matures, channels will be opened with higher limits.
setup your own node, which would need to run 24/7, in case you would like to make sure that nobody steals your money.
While Lightning Network will operate MOST EFFICIENTLY over channels that are running 24/7, it is possible and safe to shut down your node periodically as long as you are monitoring the blockchain for expired channel states more often than the predetermined lock time.
LN will encourage people to store their private keys online,
Only the keys for the funds that are in the lightning channel. Funds that have not been placed into a channel can continue to be secured with offline keys. Since a Lightning Channel transaction is a multi-sig transaction, I believe an attacker would need to gain access to private keys from BOTH sides of the channel. This is a risk, so users should consider their own risk tolerance when deciding how much value to use when opening a channel.
