Effect of serial repetition on soundness of a PCP, and what is special with 1/2?
Sequential repetition can give you any constant soundness error larger than 0, not just soundness error $\geq 1/2$.
Dinur's approach gives you a constant soundness error which is not only at least half, but, in fact, extremely close to 1, maybe 0.99999.
The note of Andrej Bogdanov that you linked to shows that getting a soundness error smaller than half inherently won't work using Dinur's approach. The reason is specific to this approach, and is explained well in the note.

The soundness amplification results work for imperfect completeness as well. It's pretty straightforward to convince yourself of that in the case of sequential/parallel repetition. Dinur's approach can also be adapted to imperfect completeness.

Remark: Dinur's approach, just like the other two approaches, requires a number of iterations/repetitions that depends on the soundness you start with and the soundness you want to get. 
In her case it's $\Theta(\log(\frac{1}{1-s}))$ iterations to get to constant soundness. Irit starts with $s\approx 1-\frac{1}{n}$, and that's why she needs $\Theta(\log n)$ iterations.