itinerary / other questions

Only in mainland Japan for 5 days and wondering about itinerary time frames and if we should get a JR Pass or use an IC card. We are very confused on best way to get from airport to Shinjuku in a timely manner.
Our biggest challenge is coming back from Mt. Fuji to get to Tsukuba Circuit. We thought we could do this in one day but by the train schedule we do not think so. ( Track closes at 6 pm.)

Haneda airport to shinjuku - day one ( multiple parties coming in different days ( Monday at 17:00 and Wed at 20:45)

Shinjuku to Mt. Fuji- (day two- train times and is there a direct route? )

Mt. Fuji to Shinjuku ( planned to stay in Mt Fuji day three and return on day four to shinjuku, but trains only come back at 15:13, 16:09 and 17:46 from what we understand. Is that right? )

Shinjuku to Tsukuba Circuit ( Is the best way to get to Tsukuba circuit is early train from Shinjuku to Sodo, the a car, bus or taxi or is there a better way?)

Tsukuba to Shinjuku ( times for the trains return?)

Shinjuku to Haneda airport ( best way, times ?)
Thank you.