Wiring – Removing baseboard heater and installing elec oven on that wall

Judging by the diagram (Fig.2) at the bottom of the 1st page on the install instructions you've linked, you should be connecting your Black L1 to the baseboard's Black, Your Red L2 to the Baseboard's Blue, and your ground to the Baseboard's Ground screw.
This baseboard heater doesn't require a Neutral for a North-American split-phase 240V supply.
You only need Live/Neutral if you have European single-phase 240V.

There's a slightly clearer version of the instructions here, with this diagram on page 2:

Replace your socket if my memory serves me right European wiring - Brown is your hot and blue is your neutral. Your socket looks heavily damaged and will cause you problems even with a new plug - it is a safety hazard. The resistance at that point is higher than it should be (think HEAT - melting eventual falling apart - loose hanging moving unshielded wires..).

I am not familiar enough with European codes to state whether you can plug it into a wall socket - the current carrying capacity of the wall socket wiring might be lower than your dedicated oven socket. If that is the case you will burn your house wiring and possibly burn your house down.

Replace your socket - it is not that difficult - but by all means TURN OFF ANY CIRCUIT BREAKERS or REMOVE FUSES that supply power to that Circuit. Test with a volt meter first to verify no power. Even when power is removed: use the one hand rule and work on the circuit as if it is LIVE!