Learn Swedish: Det klimatsmarta växthuset var hon med och ritade. - The climate-smart greenhouse, she helped design.

This is the participative pseudo-coordination you are currently learning. The phrase vara med och (to help or participate in doing something) links two verbs that must be in the exact same tense. Because the action happened in the past, both the state verb (var) and the action verb (ritade) are conjugated in the past tense.

Why is the sentence ordered Det klimatsmarta växthuset var hon... instead of starting with Hon?

This is called topicalization. By putting the object Det klimatsmarta växthuset at the absolute front of the sentence, the speaker heavily emphasizes what she helped design. Because Swedish enforces the V2 rule, the finite verb (var) must immediately follow in the second position, which pushes the subject (hon) into the third spot.

I learned that rita means 'to draw'. Why is it translated as 'design' here?

While rita does literally mean 'to draw', it is the standard Swedish verb used for architectural and engineering design. When talking about buildings, houses, or a greenhouse (växthus), att rita means to design or draft the blueprints.

What happens to the meaning if we remove med and just say '...var hon och ritade'?