Hi Whaley
Knowledgeable on public transport I am not! just happy to help out and I lived in Palma for quite a long time. Once you are in Palma in Plaza España you will be able to pick up virtually any bus travelling through the city and outskirts. To get to Carrefour in Coll den Rebassa you could use the number 15 bus, and the carrefour off the Valldemossa motorway turning again could be reached by a bus heading for Establiments or one that stops at the top of General Riera. Alcampo can be reached by the train stop in Marratxi, and a short walk (check that one out) Ikea............no idea, Calle Manacor is a major street from Plama centre but i don't know how far the bus goes up, I had a look on their website but they only give you directions for cars. As they speak English, I think that the best thing to do would be to ring them and ask what route to take via bus.
By the way, festival no longer has an ice skating rink, it's now the circus of terrors, and changes every now and then for a different attraction.
I hope that helps a bit.
Later