You only need to open a few channels to reliably connect to the network - the network allows you to transact with those you don't have a direct channel with. And in actual usage you won't ever need to close them. Lightning solves transaction costs.
Well that depends. If you run out of money, then you have to transfer more coins onto the network.
If you don't want to make frequent 'top up' transactions to what is effectively a hot wallet, then you'd have to lock away many thousands of dollars.
Transaction fees on chain still matter quite a lot if you are unwilling to lock away a whole bunch of money up front.
Also the more money that is locked away on the LN, the more vulnerable to attack it is.
This is because one can attack the network by DDoSing the main chain, such that blocks are full for the time lock period. IE, if someone cheats and publishes an old LN transaction history, you have to publish your anti cheat transaction and if blocks are full for the couple weeks, then you can't defend yourself.
This style of attack only works if there is a bunch of money in the network though.
It is also counteracted if the main chain has high capacity as it becomes that much more expensive to attack the main chain.
With the lighting network you still have to make 2 on chain transactions. 1 to establish the initial channel, and 1 to close it.
And this is PER channel that you establish.
These transaction fees could be quite high, if history is to be used as an example (only a couple months ago, fees hit something like 40 USD).