A few questions

Hello, I have a few questions around my itinerary. Would love your help to understand better if I need a JR Pass, for how long and also a couple of recommendations.

21-24 April - Tokyo
25 April - Tokyo / Hakone (if I have the JR pass, do I still need the Hakone Free pass from Shinjuku Station? Or better not activate my pass yet and buy the free pass with train ticket?)
26 April - Hakone - Kyoto (is it a bullet train? should I activate my JR pass here?)
27-30 April - Kyoto
1 May - Travel from Kyoto to HIrasaki (I assume it has to be Kyoto/Tokyo/Hirasaki. How long will it take on the bullet train?)
2 May - Hirosaki
3-4 May - somewhere on my way back from Hirosaki to Tokyo (suggestions?)
5 May - Flight from Tokyo

If I buy a 7-day pass and activate it on 26 April, I'd have to be back in Tokyo by the end of 3 May, right? Is it worth buying it for the trips on these dates or would it be less expensive to buy single tickets?

Many thanks
Ana