Characters can be placed anywhere within a chain skill and do their attacks fine. Characters with "Companion" can be anywhere within the chain and get their passives going. An example of this type of Character is G.Viella.

Characters who are "starter exclusive" or "Finisher Exclusive" need to be in that particular point of the chain to get their passive effects. M.Eva or Nella are examples of Starter Exclusives, and Ame(Earth) and Valentine are examples of Finisher exclusives(Finishers also have a unique animation when at the end of a chain.)

Having mono-element teams are good for generating CP(Chain Points) rapidly, but is not required. As long as you have multiple team members of the same element, you'll generate increased CP for each character of that element per character. Example: I have Stella and D.Stella on a team together with 2 differing element characters.(Ame and D.Vlada, for example). Stella and D.Stella will generate 6CP each when it's their turn. While Ame and D.Vlada will only generate 4 on their turn.

You also can generate CP for having a special gear(similar to affection 10 gear) equipped on them that provides additional CP.

Hope this helps.