Mt. Fuji Area Day Trip

Hello! I'm planning a day trip to Mt. Fuji on July 1 quite like some tour operators organize, however, I'm hoping to save some money and do a self-guided tour instead. This is what I'd like my itinerary to be like
1) Shinjuku to Kawaguchiko 5th Station by bus to visit Mt. Fuji
2) Somehow get to Togendi Station then take a 5 min walk to Kojiri Pier for the Lake Ashi Ferry Boat Tour
3) Get off at Hakone-en Pier
4) Hop onto the Mt. Komagatake Ropeway and get off at Odawara Stn
5) Head back to Shinjuku

I have some questions mostly about travel and transporation

1) Does the 6x a day bus schedule start immediately on July 1 or is it closer to the middle/end of the month?
2) How do I get to Togendi Station from Kawaguchiko 5th Station?
3) Once I get onto the Ferry boat, is there an actual Hakone-en Pier/Stop to get off at?
4) Is the Hakone-en Pier/Stop where I would be able to get onto Mt. Komagatake Ropeway?
5) How do I get back to Shinjuku the cheapest and fastest way from the Mt. Komagatake Ropeway?

Also, if I'm not planning on ascending Mt. Fuji, but just seeing it, is Lake Kawaguchi be a better place to go than the 5th station?

Thanks!

After talking to some people, seems like Kawaguchiko 5th Stn isn't all that interesting to go see if I'm not climbing the Mountain. I'm planning to just go to Hakone Area (specifically the Boat Ferry and hopefully the Mt. Komagatake Ropeway). Any suggestions on where to go around that area and how to get there from Shinjuku. Also, is the Hakone Free Pass the best way to travel to all these places?

Thanks!

Does the 6x a day bus schedule start immediately on July 1 or is it closer to the middle/end of the month?

Yes, the bus from Shinjuku to the 5th Station starts at its climbing-season shedule from July 1.

How do I get to Togendi Station from Kawaguchiko 5th Station?

I assume you mean Togendai at the shores of Ashinoko in Hakone:
1) Take a bus from Kawaguchiko 5th Station to Kawaguchiko Station
2) Take a bus from Kawaguchiko Station to Gotemba Station
3) Take a bus from Gotemba Station to Togendai.

It takes about three hours.

Once I get onto the Ferry boat, is there an actual Hakone-en Pier/Stop to get off at?

Yes.

Is the Hakone-en Pier/Stop where I would be able to get onto Mt. Komagatake Ropeway?

Yes, the boat pier and ropeway station are close to each other.

How do I get back to Shinjuku the cheapest and fastest way from the Mt. Komagatake Ropeway?

Probably by direct Odakyu Highway Bus.

Also, if I'm not planning on ascending Mt. Fuji, but just seeing it, is Lake Kawaguchi be a better place to go than the 5th station?

The views of Mount Fuji are better from the base around Lake Kawaguchiko than from the 5th Station.

Also, I recommend against doing all of the above within a single day. You would be spending more than half of the day on board of buses. I recommend to spread it over two days or participate in a guided 1-day bus tour from Tokyo that travels a similar route.