Transportation logistical questions for upcoming Denmark trip

Is it recommended to reserve seats in advance for: Train from
Copenhagen to Svendborg. Train from Svendborg to Odense.

From Copenhagen to Odense it can be a good idea depending on when you travel. Odense to Svendborg is local train and I'm not even sure it is possible to reserve seats there. But if you are only planning one trip per day, those passes sound like a waste of money to be honest.

In Odense we are picking up a rental car at Avis address is
Groenloekkevej 8c. Does anyone know if this is walkable from train
station? Or is far enough that we should take a taxi?

There are many great map sites on the internet that can answer that question. But yes, by European standards at least that is perfectly walkable. But you can also take the tram, no need to pay for a taxi.

we will be dropping it off in Frederikshavn on another day as we will
be taking the overnight boat to Norway from Frederikshavn. Is anyone
familiar with this boat terminal and the location of the Avis Rental
(Koktvedvej 27)? I am wondering since we will be dropping off in the
evening how we will get from the rental car facility to the boat
terminal. Wondered about public transportation in this area?

How late? You can take local bus 13 to Rimmenstorvet and walk the last bit, but it doesn't run very late. Or you can take some other bus routes, you can find the local buses and trains at https://www.nordjyllandstrafikselskab.dk

From car drop off to ferry it is about 1 mile so not impossible to walk even with luggage.