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Does each dot represent the (approximate) Geolocation of a node? Or is it only right up to the country level? I mean in the US, the brightest dot falls in the middle, likely in Kansas state, is that reliable?
Mempool uses the MaxMind GeoIP database. It attempts to map every public IPv4 or IPv6 address to a country, state, city. It's not perfect, but pretty accurate.
However, most LN nodes use Tor only and don't have an IP address to track. Additionally, some nodes have many IP addresses in different countries. Nodes can also trivially set up a proxy to make their IP address look like its coming from the country of the proxy and not the country where the actual node hardware is hosted.
The vertices represent the connecting channel, with the amount? Does it mean any transaction below the amount is likely to pass through between those nodes?
No. That's capacity, for a tx to work, you need liquidity in the direction of the payment.
I am not a node runner, but use custodial lightning sats with the Blockstream Green android app. Can I find a node corresponding to Blockstream and its channels?
Maybe blockstream's node is one of these: https://amboss.space/search?term=YmxvY2tzdHJlYW0=
You can generate an invoice using your wallet, and paste it into lightningdecoder.com. It will tell you the pubkey of the destination node for that invoice.
Suppose a pay at a coffee shop in Hong Kong using Blockstream green. How do I figure whether the node has liquidity to handle the transaction?
Only way to know is to try! You wallet will attempt dozens or hundreds of possible paths looking for one with sufficient liquid to process the payment. Most wallets will automatically make the payment once it finds a route. However, if you're a wizard, you can probe the path first to see if there is liquid without actually sending the payment. This involves custom route building and crafting custom onion htlcs.