I would suggest to try to not use rail planner app, because it shows the interrail.eu website for reservations.
Kiel-Mannheim or Frankfurt (I don’t know where you have to change trains) you don’t need a reservations on day trains in Germany. You can book one for 4€/trip via bahn.com seat only option or 3€/train via ÖBB tickets.oebb.at - seat only option.
Frankfurt/Mannheim-Paris you need a reservation, this is online only bookable via Interrail.eu or the app. Or at ticket desks of Deutsche Bahn. (about 10-15€ reservation).
Reservations France-Barcelona are only possible on ticket paper. This means when you buy it via App or Interrail.eu you get it by mail at home. Or you can buy it also at desks of Deutsche Bahn in Germany or SNCF in France. This trains have quota for Interrail users, this means it can be easy booked out for Interrail user. (35€ reservation)
Lyon-Nice-Ventimiglia use TER regional service. You don’t need a reservation.
Ventimiglia-Milan you can use Intercity IC (3€ reservation) or Frecciabianca (10€ reservation), or with one change in Genova without reservations to Milan with Regionale Veloce RV trains. Reservations for Italy bookable via Austria Railways via tickets.oebb.at with this instructions (one way ticket - discount Interrail)
Milano-Basel 11€ in 2nd class reservations bookable via ÖBB via tickets.oebb.at
Basel-Hamburg you can use the nighttrain ÖBB Nightjet for couchette or sleeper or on the same train the seats (reservation optional) of the Intercity IC part (4€/trip via bahn.com or 3€/train via ÖBB tickets.oebb.at - seat only option)
For Denmark-Hamburg trains, in summer you need a reservation (but I don’t know if this is up-to-date), but if you need a reservation than you can’t book via Deutsche Bahn bahn.com but you need to get via DSB the reservation.
From Copenhagen use the Oresund trains wich you can use without reservations to Göteborg.
P.S. for reservation optional trains in Germany, Switzerland and Denmark you can buy one reservation for 4€ also when you change trains via bahn.com seat only option. Railplanner/Interrail.eu ask 6€/train.