1) Will signature aggregation / Key aggregation be available for legacy addresses that start with '1' or are these only for multi-signature addresses that start with 3 or bc1? If not, could somebody explain to be in an easy to understand way on why is this the case?
It will likely only be available for addresses beginning with bc1, and even then it won't work with all addresses that begin with bc1. Rather it will likely only work with those addresses which encode another witness program version (the current ones are for witness version 0). This is because introducing signature and key aggregation will need to use new script opcodes which are more easily introduced via a soft fork in a new witness version. Basically, since Bitcoin does not currently support key or signature aggregation, new script opcodes will need to be created that do support those things and the only way that they can be used is if new outputs use them. Thus all current outputs that do not use those currently nonexistant opcodes will not be able to use signature or key aggregation.
Note that this is not a guarantee. There has not yet been a proposal for implementing this in Bitcoin. All that we have so far is just the cryptography itself. So perhaps someone will think of a way to make key and signature aggregation work with old outputs.
2) I've tried opening a lightning channel using the lightning-app on testnet, I really loved playing around with it and am Impressed with the instant payments. I was wondering if anyone else could send me ligthning payments (me receiving them) if my channels were already fully funded and the 'Available to receive' is '0'. If this were to be the case, would the sending party have to independently open a new channel with me to send me the funds instead of having to rely on existing channels?
If the other party in all of your channels has a balance of 0, then you cannot receive Bitcoin. What would need to happen is that you either transaction and send money to someone else thus moving funds to the other person in your channel, or someone opens up a channel with you and they fund the channel.
3) Will the users be allowed to set an nLockTime or a time period after which the channels will be automatically broadcasted to the bitcoin network and closed? Currently I've tested Eclair for android, lightning-app and Bitcoin + lightning wallet for android and they all seem to not provide this option. I'm assuming it's a 'To be developed' thing?
AFAIK, currently you cannot do that. But there's no reason why that can't be implemented in the future.
4) Will I need a lightning node with a public IP broadcasted in order to be able to earn from fees for nodes using my channel to transact between each other?
No. So long as you have channels established with other people and have active connections to other nodes, you can be chosen to be part of a route without accepting incoming connections.