how complicated to build an AR

there is building an ar and assembling an ar.. What you describe is simply assembling. Building would include machine work. Generally easily available components such as stripped uppers ,lowers, bolt carrier groups and receiver kits can be had economically. On several occasions i have done the machine work tochamber and fit a barrel with good results. Not really worth the trouble with so many high quality components available.
When assembling the various pins,springs ,detents etc it is not uncommonto have something get away and fly off in space. I often do those assembly operation in or thru a large zip lock bag if possible.
In any case go for it . You will have fun.
 
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