1. 4 mm² for each of the 3 wires
2. C25 or C20
3. Direct wiring with disconnect switch, commando plug or round pin 15A socket + plug

If TS's thread picks up steam, you are going to have a lot of differing opinions on what you are asking.
But my personal opinion is that if you understand the safety issues, limitations, and the repercussions, then your extension is possible. It is entirely your responsibility at the end of the day anyway.

You could make sure only one appliance is used at a time by using 2 plugs and 1 socket, so that only one appliance can be used concurrently. Use quality 15A plugs and sockets only, so that an appliance cannot be inadvertently plugged into another socket. Or use a permanently attached change over switch (but it's a bit ugly)

This is not allowed by code in Malaysia. Only wiring larger than 16 mm² may use a Earth wire that is smaller than the power conductors.
(Disclaimer : this is off the top of my head, getting ready for something so reluctant to look for the actual size of wire but it is something like that. Maybe it's larger than 10 mm²?)

You want to save money by using 2.5 mm² Earth wire then that's on you.

Actually can use 2.5 mm² wires, as 3000 W will use under 14 Amp. 2.5 mm² wires are rated at 20 A so should be quite safe. Just ensure the wire is a branded that follows the proper specifications and the size is actually 2.5 mm². Make sure the MCB is C20 if using this size wire. I would use a maximum oven if using 2.5 mm² wires up to 4000 W.