transactions – How to select intermediate nodes (payment service providers) in Lightning Network?

I raise important questions about Lightning Network terminology and the selection of the intermediate node as a payment service provider in a routing channel:

The following video (Link to the video titled "How Bitcoin Lightning Channels Work") assimilates the LN channels to abacus such as channels are like rods comprising beads like bitcoin this slide from one end to the other, something similar to the following figure:

A Lightning Netword channel between A and B.

Where, in this example, the user A has 2 pieces and the user B, 1 piece.

This video also states that:

"There is no way to add more pearls or remove some of the
beads
without taking the stem all together. "

And if that expression is correct, it means that the channel capacity is always equal to the channel balance, while this answer (Link to reply) distinguishes between the channel capacity and the channel balanced as following:

  • the capacity is the amount of Bitcoin provided to this channel.

  • the balanced encodes the amount of bitcoins that each channel partner has in the channel. so the sum of the balances will always be the
    total capacity of the channel. *

Whereas the description of the video (that is to say "There is no way to add more beads or remove a part without having dismantled the stem.") means that the capacity is always equal to the channel balance.

As a first question: Which expression is correct?

In the meantime, according to video, the condition for choosing a intermediate as the Payment Service Provider is as follows:

If the users A and B have a direct channel AB and the users B and C have a direct channel BC, so that the user A has 3 pieces in the channel AB and the user B has 2 pieces in the AB channel and 1 piece in the channel. BC channel. Suppose then that user A wants to send 3 pieces to user C. The situation is as follows:

Selection of the qualifying intermediate node as a payment service provider.

We now want to determine if user B can be an intermediary as a payment service provider, according to the example mentioned in the video:

Although the user B has a direct channel with the user C and usually 3 pieces in both channels A-B and B-C; however, the user B can send only one piece to the user C; user B can not therefore be selected as a payment service provider (intermediate node). Users A and C must establish a direct channel between them.

If the expression above is correct, then we can define the conditions of an intermediate node as follows:

(1) The intermediate node has a direct channel with a destination or another node that has all the conditions of an intermediate node.

(2) If the amount of the transaction equals n coins, the intermediate node has at least n coins payable to / in the direction of destination.

Second question: The above conditions for the selection of
eligible intermediate node as a payment service provider