Scenario 1: Fighter makes two attacks with his two longswords.
Scenario 2: Alchemist makes two attacks with his two longswords.
Scenario 1: Fighter drops one and take the free hand and grips the longsword, now gaining bonus damage from two handing it.
Scenario 2: Alchemist raises his vestigial arm to grasp his longsword, now gaining bonus damage from it. He still gets two attacks because he is still wielding two blades, but has not gained any "additional attacks".
Scenario 1: Fighter drops longsword and picks up greatsword, which requires two hands to hold, just like he did just a second ago with the longsword.
Scenario 2: Alchemist drops longsword and picks up greatsword, which requires two hands to hold, just like he did a second ago with the longsword. However, he also drops his second longsword and picks up a second greatsword, mimicking the mechanics allowed with the first pair of hands. He still gains no extra attacks.
The alchemist is using the "arm can wield a weapon and make attacks as part of the alchemist’s attack routine" option. He is gaining no new, extra, bonus, or additional attacks. He is simply using the strength from the vestigial arm to "wield a weapon and making attacks as part of his already existing attack routine".
Edit: You are still TWF, just with improbable weapons.
