Osaka-Kobe-Kyoto-Oita-Tokyo

My husband and I will be visiting Japan. We plan to visit Osaka (3 nights), Kobe (day trip while staying in Osaka), Kyoto (3 nights), Oita (2 nights) and Tokyo (2 nights) in October 2019. Questions: (1) we shall buy 14 days JR pass? (2) do we need to buy additional pass while visiting Osaka / Kobe / Kyoto? Which one? (3) will these passes include local transportation e.g. metro / local train / bus etc?

(1) we shall buy 14 days JR pass?

I don't think so. Since your long distance travel is Kyoto to Oita and Oita to Tokyo, you would better consider flights. ANA or JAL's promotional fare for foreign tourists should be around 60 USD for Osaka to Oita (Kyoto has no airport, nearest one is in Itami/Osaka) and 100 USD for Oita to Tokyo. Further Oita to Tokyo is very long train rides which will take 3 hours more time than flight.

(2) do we need to buy additional pass while visiting Osaka / Kobe / Kyoto? Which one?

It depends on your actual travel plan, but in most cases, no, you don't need pass. Just IC card will suffice. In this case ICOCA card will be suitable.

(3) will these passes include local transportation e.g. metro / local train / bus etc?

JR pass covers JR train lines. There are many non-JR metro/train/bus so these are not covered.

Shin-Osaka to Oita stations is 17,xxx yen each way. X2.

14,xxx for most expensive option for Shin-Osaka to Tokyo.

Just these three trips eclipse the cost of a 46,xxx yen 14 day pass.

Add in airport transfers and Kobe trip. I think a 14 railpass would pay off.

I have not made it more clear for this trip. We would like to take bullet train from Kyoto to Oita (or nearby). Is it possible? Then we have already booked a flight from Oita to Tokyo, this leg will not take train.

Then you dont need a pass.

Shinkansen to kokura station, then limited express sonic to Oita.

I have not made it more clear for this trip. We would like to take bullet train from Kyoto to Oita (or nearby). Is it possible?

As hakata14 stated, it is possible. A cheaper option is flying from Itami airport to Oita airport. The flight is less frequent and you need pre-booking for the cheap fare though.