Should we book train tickets before arriving?

We will visit Japan in the first 2 weeks of April 2018. Do we have to book train tickets before we arrive to japan? These are the trains/buses we plan to take:
A train from Tokyo to Takayama on the day of Spring Festival.
A Bus from Takayama to Shirakawa on April 15th - the day of Spring Festival.
A train or bus from Shirakawa to Kanazawa.
A train from Kanazawa to Kyoto.
A train from Kyoto to Osaka.

Tokyo to Takayama = only Tokyo to Nagoya can be booked online using the tokaido/sanyo shinkansen app. Nagoya to Takayama need to be done once in Japan.

Buses you can do in advance from memory. I think Nohi bus lines.

Kanazawa to Kyoto = can only book once in Japan. But also has non reserved seating.

Kyoto to Osaka = no need as only commuter service is require.

My friend and I are coming to Japan in May and I have booked bus travel from Takayama to Kanazawa via Shirakawago online through Japanican. It was very easy to do, although I had to set up an account first before the booking.

You do not have to book, but looking at your schedule, the Takayama spring festival is going to be the difficult one for availability. If you wait until you get to Japan it may be sold and only crowded non-reserved (standing) space available. Too early to tell as the bookings for that do not open until 15th March (one month before).

Similarly for the bus to/from at that time of year. With the large numbers attending the festival, getting a booking could be hard.