You will find winter conditions: short daylights, snow and icy conditions.
Rental car is a good question.
Basically you have two options:
- North: Alta, Hammerfest, Magerøya, North Cape (along E6, later E69)
- South: Lofoten and Vesteralen, maybe Senja but the summer ferry to Andenes starts in May
Lofoten are known for their beautiful landscape.
For watching NL I would follow the clear sky forecast because this is what you need when they appear.
Another option is to book port-to-port on Hurtigruten / Havila ships which is very comfortable (and warm), e. g. Tromsø - Kirkenes - Tromsø (North) or shorter Tromsø - Svolvær - Tromsø with nights of Lofoten in between.
Can some expert help to suggest/draft a travel plan ?
I am not a fan of this approach because people normally get money for this service. Please search in Norway and in trip reports forums for itineraries to / from Tromsø and post an own first version asking for feedback.