After soldering, the insulation of the wire has melted slightly, is this allowed for class 3?

Yes that is allowed. It’s almost impossible that this will not happen. Due to the heat from the soldering iron, the insulation always melts slightly backwards …..unless you use a heat shunt (heat sink) or a heat-resistant insulation (such as Kapton/Teflon). The insulation may melt but not burn / char. For detailed pictures see IPC-A-610 or the IPC/WHMA-A-620 standard.