Tokyo to Hakone-Yumoto to Fuji Five Lakes

We are traveling from Tokyo to Hakone and Fuji Five Lakes and we are using the 3-day Hakone Fuji Pass.

1] Which is the best option should we take?

a) Day 1 - travel from Tokyo to Hakone [stay 1 night at Hakone] ;
Day 2 - travel from Hakone to Fuji Five Lakes [stay 1 night at Fuji Five Lakes];
Day 3 - travel from Fuji Five Lakes to Tokyo
or
b) Day 1 - travel from Tokyo to Fuji Five Lakes [stay 1 night at Fuji Five Lakes];
Day 2 - travel from Fuji Five Lakes to Hakone [stay 1 night at Hakone]
Day 3 - travel from Hakone to Tokyo

2] Also, what mode of transport should we take from Hakone to Fuji five Lakes and vice versa?

Please enlighten.

It is actually rather difficult to travel between Hakone and the Five Lakes area, there are no direct train pathways and the only way of commuting between the two using the Fuji Hakone Pass is to take a bus to Gotemba then swap to another one to reach your destination.

Between the two areas, I recommend staying at Hakone and doing Kawaguchiko as a day trip, as there are many more hotels/ryokan in that area and a greater abundance of things to see and do. It is also much more convenient to travel from Shinjuku to Hakone(Odawara) using the Romancecar, which has trains every 20 minutes, while the trains from Fuji Five Lakes to Tokyo are much more infrequent. I personally prefer riding the highway bus to get from Kawaguchiko back to Tokyo instead.

I'd recommend doing the Owakudani ropeway, museum hopping in the town of Gora and hot springing either at your ryokan or at the Yunessun resort.

Thank you so much for your quick response.

In this instance, will it be better to do a day trip from Tokyo

Day 1 ~ travel from Tokyo to Hakone and then back to Tokyo;
Day 2 ~ travel from Tokyo to Fuji Five Lakes and then back to Tokyo

https://www.japan-guide.com/e/e2358_014.html

This pass is perfect for your initial 3-day itinerary.
Just note that currently the Hakone Tozan Railway is not in service (there are buses instead).