Additional strikes?

To match the current rules and clarifications, the rulebook should be written this way (or something approaching):

Additional Strikes: Some cards and effects allow a minion to make additional strikes during the current round of combat. Additional strikes are announced (gained) and performed (used) only gained after the first pair of strikes are completed has been resolved. The acting minion decides whether or not to gain additional strikes before the opposing minion, as usual. Additional strikes are handled by having another choose strike phase and resolve strike phase in which only the minions with additional strikes may play strike cards. All additional strikes take place at the same range. This is repeated as necessary. A minion cannot use more than one card or effect to gain additional strikes per round of combat. Some effects grant additional strikes that do not count against this limit; in that case, any extra source of additional strikes are gained only after the last pair of additional strikes gained by the minion has been resolved.

ICL wrote:

How do all of these proposed changes interact with first strike?

It doesn't change anything. Strikes with first strike are declared as normal, and resolve before any classic non-first strike in the same pair of strike (but is "beaten" by dodge and s:ce as usual).