I have a question about the word 设计. Can the second character 计 be pronounced with a 轻声? (is it correct or common to do so?) I notice that 轻声 for a lot of words isn't always included in the dictionaries.
Yes. That's the typical feature of Northerner's Mandarin. Although not marked in dictionaries, pronouncing she4ji0 is natural for Northerners, same to many other words.
When I studied English, I find many AE pronunciations also deviate from their transcriptions. Their accents may move according to the tone of speech. And, many people say inte.RES.ting instead of IN.teres.ting (dictionary standard)…
I don't think I've heard the word "interesting" pronounced with the primary stress on "res" instead of "in" before. The secondary stress should be on "res" though. (Pronunciations do vary considerably by region though so maybe it is pronounced with the primary stress on "res" in some places!)
The word 设计 can be interpreted in two different ways:
1. "design". Both she4ji4 and she4ji0 are OK to me.
2. "design a stratagem" (设计 is short for 设下计策). Both characters must be stressed and the 4th tone.
Personally I would usually pronounce 设计 as
she4 ji0 (the first meaning, the 轻声 is like a light 4th tone) or
she4 ji4 (the first meaning) or
she4 ji4 (the second meaning, 计 is even more stressed than above).
So the sound of 计 ranges from a very light 4th tone to a very stressed 4th tone...