Getting to Fuji Five Lakes

This travel forum is wonderful. It has provided me with insight to plan for my 1st F&E trip.

Hope you can help me with my planning. I have JR pass and plan to travel from Kyoto to Fuji Five Lakes for a night stay at Lake Kawaguchiko area before going to Tokyo. My plan, on a weekday, is as follows:

Day 1
0856 Kyoto to Shizuoka by JR (H464)
1048 Shizuoka to Shin-Fuji by JR (K640) (Arrive abt 1107)

Option 1a –
Shin-Fuji to Shiraito Falls by Fujikyu bus (1230)

Option 1b -
Mishima to Shizuoka-bound JR Tokaido Line local train to Fuji station, change again to the JR Minobu Line for the final run to Fujinomiya.
Fr Fujinomiya to Shiraito Falls by Fujikyu bus (The bus shd leave Fujinomiya at 1305)

1515 Shiraito Falls to Ice Cave by Fujikyu bus
1642/ 1717 Ice Cave to Kawaguchiko by Fujikyu bus
(pickup by hotel)

Day 2
Kawaguchiko to Tokyo

Option 2a – (est 3 hrs+)
Fujikyu bus to either Shinfuji or Fujinomiya
Shinkansen to Tokyo

Option 2b -
Fuji Exp. Fujisan Ltd.Exp.12 to Otsuki
Ltd Exp. Kaiji 114 to Shinjuku
JR Chuo line to Kanda (Tokyo)

Qns:
Day 1 - Which route would be better? Option 1a or 1b? If I take the Mishima route, would it be cheaper? would it be possible to catch the bus at 1305?

Is there any large coin lockers in JR shin-fuji and Mishima? How about Takkyubin counters?

Is there any day pass i can use for the fujikyu transport?

Day 2 – Which route would be better? Option 2a or 2b? Are the transport mentioned in option 2b covered under JR pass?

Thanks in advance for you help!

I am not sure when you will be traveling, but note the closing times of the Ice Cave, which can be as early as 16:30 in some winter months:
http://fujigoko.info/icecave/info-time.html

Which route would be better? Option 1a or 1b?

You wrote it yourself. 1a is more convenient. 1b is cheaper. It comes to personal preference.

Is there any large coin lockers in JR shin-fuji and Mishima? How about Takkyubin counters?

I am not sure about the size of lockers available, but I think that most shinkansen stations have at least some large lockers. I doubt that either station has a takkyubin counter, but note that you can also send them from many convenience stores, some of which can probably be found near the stations. However, if you use takkyubin, I strongly recommend to do so from your hotel in Kyoto!

Is there any day pass i can use for the fujikyu transport?

Yes, they are introduced here:
http://www.japan-guide.com/e/e6905.html

Which route would be better? Option 2a or 2b?

Definitely 2a.

Are the transport mentioned in option 2b covered under JR pass?

Not the bus portion of it.