Required conditions to be selected as intermediary node (Payment Service Provider) in Lightning Network?
Note that this video is made by shitcoin paddlers trying to spread FUD. If I remember correctly the further episodes are much much worse.


  "There's no way to add more beads or take off a portion of the beads
  without taking the rod down all together."


This is false. It is possible to both add and remove coins from a channel. It's called topping up or splicing. Having all your coins on one "abacus" is pointless. So who cares if you have 10 channels that you close one to pay something onchain? (Possibly using the same transactions to re-open the channel immediately.)


  this answer (Link to answer) distinguishes between the channel capacity and the channel balance as follows


I think you're reading that answer wrong. Of course capacity is different from balance as capacity is one number and balance is 2 numbers. Also note that "capacity" is a nice thing to talk about when talking about the total capacity of the whole Lightning network (as sum of all channel capacities) but the capacity of a single channel is kind of pointless. I'd argue it's actually more informative to define a channel as having two capacities: one in each directions. So your first drawing would have 2 + 1 as capacities. With this definition you can talk about the capacity of one channel in a certain direction as well as the capacity of a whole path from payer to payee over multiple channels (and a different capacity in the reverse direction). The total capacity of the whole network would still be the same.


  So, user B cannot be selected as Payment Service Provider (intermediary node) and users A and C have to establish a direct channel between themselves. 


False in two ways. 1) A can use this path for 1 BTC and send the rest over another path. 2) A and C don't have to connect to each other, they just need to have a few more channels. This is called Lightning Network after all.


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


Sounds correct.


  (2) If the amount of transaction is n coins, the intermediary node has at least n coins payable towards/in the direction of destination.


Yes. I'd even say "each intermediary node" (not "the") as according to (1) there can be more than one. But note that the payer always has the option of splitting "n" up into "n1 + n2", sending each over different paths.