I'll assume you have something like this:
simulate this circuit – Schematic created using CircuitLab
If you don't, then do provide more information.
When charging is a fuse needed? I'd say yes! Basically, fuse is there to protect the battery from being damaged by the load. Batteries can often provide large current when shorted and if somehow the load gets shorted, battery would be protected by the fuse from the short. If the battery is charging, and the load somehow gets shorted, then you'd have even worse situation. Not only would battery provide current for the short, but charger would as well. The result would be melting cables and damage to the battery and the charger due to overcurrent.
Next, about the "positive" part. That, as always, depends on perspective since voltage needs a reference point. I'd call positive terminal of the battery positive and I'd call the terminal of the charger connected to the positive terminal of the battery positive as well. They're both more positive than their own negative terminals and are commonly marked as positive, which means that others will easily understand about which terminal you're talking.
If you explained to us why you want to know which terminal would be which, we could provide more information. For example if you measured voltage between the positive terminal of the charger and the positive terminal of the battery, while the charger is running, you'll see that the charger's terminal is more positive than the battery's positive terminal (making the positive terminal of the battery negative). In such situations I'd still keep the designations I introduced in previous paragraph since changing them could add confusion into conversation.