So then why do we need a textual derivation for the rule that an agent can appoint another agent? It should be enough that the second agent knows what the sender wants and is acting beneficially on his behalf.

First, it is possible that the sender is particular and wants specifically the first one. Second, perhaps that itself is what is derived from there. After all, there is such a thing as a general appointment of agency: whoever wants may do such-and-such for me. Apparently, in ordinary agency the sender may be particular about the identity of the agent.

And in fact, the commentators disagree whether the second agent is the agent of the sender or of the first one.
It should be remembered that in mere words this does not help. There are rules in the Torah’s laws of agency beyond the sender’s will.

1) If the sender is particular and wants specifically the first one, then an agent cannot appoint another agent. It is hard to say that the Torah introduces the novelty that there is no such particularity.
2) According to the view that acquisition on behalf of another operates by virtue of agency, why do we need a derivation both for acquisition on behalf of another and for an agent appointing another agent? I can understand why we would need a derivation for both agency and acquisition on behalf of another, since if there were only one derivation I would derive agency that does not include acquisition on behalf of another; but once I have learned acquisition on behalf of another, why do I need the rule that an agent appoints another agent?
3) According to the view that acquisition on behalf of another operates by virtue of agency, why is it impossible in the case of mere words?

1. It is not difficult. The novelty could be that we are not concerned about that. Beyond that, the novelty is that one can create a state of agency, because as I said, Jewish law has constraints beyond the wishes of the parties.
2. Same as above.
3. This is not the place to get into the topic of mere words.

So according to the one who says that acquisition on behalf of another is by virtue of agency, and that acquisition on behalf of another means we are effectively certain that he made him an agent, then apparently this is exactly like agency with an appointment. Does he still agree that the agency involved in acquisition on behalf of another is different from ordinary agency? Why should it be different?

I did not write that this is a case of our being effectively certain. On the contrary, I wrote it as two different possibilities.

According to Tosafot in Ketubot, who hold that acquisition on behalf of another is agency based on our being effectively certain, is there a difference between an explicit appointment and acquisition on behalf of another with respect to the constraints you wrote about that exist beyond the wishes of the parties?

Tosafot apparently hold that an appointment is required, and therefore in the case of acting beneficially on someone’s behalf too, in their view there is an appointment. But if one understands that an appointment has no formal requirement and serves only to ascertain the sender’s wishes, then there is no need to say that in acting beneficially on someone’s behalf there is an implicit appointment. For example, Rabbi Akiva Eiger writes in Ketubot that the rule of acting beneficially on someone’s behalf applies to a minor because this is a form of agency that does not require an appointment. If there were an implicit appointment there, that would not apply to minors either.
Therefore דווקא according to Tosafot there is such a difference, since they hold that a formal appointment is required, and not that the appointment is merely a disclosure of the sender’s wishes.
However, one could say that the sender’s wish being discussed is his wish that that particular person carry out the agency, and not merely a wish regarding the content of the agency. That brings us back to the discussion above.