I can't answer all your questions but I can try for a few. The impacts are different events from what I've gathered, the first impact is Adam crashing into the earth, the second is caused by the katsuragi expedition and the third is the fusing of Adam and Lilith. There were two methods that were running alongside one another in NGE trying to initiate third impact and Human Instrumentality. Gendo's and Seele's. Gendo intended to use himself as a vessel of Adam (having Adam in his hand) and rei fused with Lilith in central dogma so the he would be the "focus" or "controller" of human instrumentality all so that he could meet yui again using her soul in Eva-01, rei refused him and it failed. Seele intended to use the MPE's and lances to remove the AT fields and turn everyone into an ocean of LCL, this would have given the same instrumentality as Gendo but without anyone person as a focus or controller, just one massive hivemind. What actually happens is rei takes Gendo's hand (with the Adam embryo) and fuses with Lilith, then takes in Eva-01 and Shinji after the MPEs caused it to fuse/become the tree of life. The rei+adam+Lilith tangs everyone (turns then to LCL) and pretty much becomes god. Then it fuses with Eva-01, which became the tree of life as a result of the lances and the MPEs AT fields, and the instrumentality is implemented. Shinji becomes the focus because he is the only soul with an AT field in the rei+Adam+Lilith+eva+Shinji mess that is created. Then the events of episodes 25/26 occur inside and after some trippy visuals we get the iconic scene with the ocean of LCL, rei's giant head and Shinji and Asuka.

Some of this is just my own interpretation and speculation (mostly the Shinji stuff) so don't crucify me if I'm wrong.