When Sovereign assigns new tokens to the three ships chosen, do they all have to receive the same type of token or can it differ ship-by-ship? The wording "token of any type" seems a little ambiguous to me.

It doesn't actually "assign" them. You discard any token and it can be of any type.

6 hours ago, Npmartian said:

When Sovereign assigns new tokens to the three ships chosen, do they all have to receive the same type of token or can it differ ship-by-ship? The wording "token of any type" seems a little ambiguous to me.

This means you can change any token you currently have to any other token, it does not grant new tokens.

Is the Ship with the Sovereign title allowed to be one of the three ships at distance 1-3 to have a token discarded and replaced?

50 minutes ago, ShoutingMan said:

Is the Ship with the Sovereign title allowed to be one of the three ships at distance 1-3 to have a token discarded and replaced?

Sovereign:
"At the start of Ship Phase, you may exhaust this card to discard 1 command token from up to 3 friendly ships at distance 1-5. If you do, each of those ships may gain 1 command token of any type."

Each ship is friendly to itself. Unless the word "other" is there, the Sovereign can use the effect on the own ship.