Learn Swedish: Vem var med och köpte solpanelen i fjol? - Who was involved in buying the solar panel last year?

This is the core rule of pseudo-coordination with vara med och. The verb after och must match the tense of the first verb. Because the sentence uses the past tense var, the second verb must also be in the past tense: köpte. You are literally saying 'Who was with and bought...'.

How does var med och change the meaning compared to just asking Vem köpte solpanelen?

If you ask Vem köpte solpanelen?, you are asking who the sole buyer was. Adding var med och changes it to 'Who was involved in buying...' or 'Who helped buy...'. It emphasizes that the person participated in a shared action.

Is i fjol exactly the same as förra året?

Yes, i fjol is a very common, idiomatic synonym for förra året (last year). You will hear it constantly in everyday Swedish, so it is a great phrase to add to your active vocabulary.

Which words get the emphasis when speaking the phrase var med och köpte?

The stress falls on the particle med and the main action verb köpte. The words var and och are unstressed. In natural, fast speech, och often sounds just like a short 'å'.