Good morning Stan,

>1. How do I select the nodes to peer with?

By whatever selection criteria you wish.

In practice, lnd offers an "auto-pilot" where it selects peers to channel with 
automatically using some heuristic (which I do not know).  My understanding, 
c-lightning will eventually offer a similar feature at some point in the future.

Presumably node gossip will let you learn of other nodes that you might channel 
with in the future.

>2. How do I make them to do deposits - ideally I want them to match $100 each.

Currently, channels are initially single-funded.  There is a proposal 
https://github.com/lightningnetwork/lightning-rfc/pull/184 for dual-funded 
channel setup, but did not make it into 1.0.

>But since they are presumably already sufficiently connected to
>the network, why would they lock more funds?

It helps to consider that you are not particularly special, and neither are the 
existing nodes on the network particularly special.

If you have a reason to open a channel to an arbitrary node, then other nodes 
have a reason to open a channel to an arbitrary node, which might be you.  Even 
if the network grows large, that also means there are more participants who 
might decide, via whatever heuristic, to channel to your node.

If you intend to connect for the purpose of becoming a hub and earning routing 
fees, if you have some onchain bitcoins you can afford to invest, then it is to 
your interest to channel with relatively new and low-connectivity nodes. Such 
nodes might receive payments and if you are one of the few routes (or the only 
route) you then get a higher chance of being routed through.  Inverting this, 
if you have a new node with a few channels, others aspiring to become hubs will 
want to lock spare funds to channel to your node in case you become a very 
prolific user (sender or receiver) of the network in the future.

>3.  How do I find out if someone wants to connect to me?

The node connects to yours and sends channel funding messages.

Regards,
ZmnSCPxj
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