These are more difficult.
I don't think there is any more error based on neighbor bases. This is a guess.
I don't think certain sequences are more error prone. This is a better guess.
As far as amino acids are concerned, the answer is probably more "yes" than "no". Since organisms have preferred codon usages and rare codond are translated more slowly there could be a difference there. In addition not all tRNAs will probably bind their codons with the same binding energy and so that could also cause a mistake in amino acid insertion. But since making a mistake with putting in the wrong amino acid does not affect the gene, the defective protein will be recycled. Protein turnover rates can be quite rapid, but some are slow, but they all get turned over.
You ask interesting questions 8-)
Aye, that's what got me thinking. Look at "rational drug design" where one selects various candidate substrates for high scores on binding to the active site of an enzyme...
By definition you have any number of candidates which bind more or less tightly to the site, some better than others.
In a biologically active system, one may attempting to tie up the active site of an enzyme with the drug molecule in order to prevent the enzyme from acting upon its 'naturally occuring' target; and of course there are other effects such as the drug interfering in other places, etc...
The analogy to protein construction (and even to building DNA) is that while the "proper" match is energetically favorable (the high score in the docking), there is nothing to forbid a different base pair, or amino acid from arriving first.
[Many deeper thoughts and pretentious drivel deleted...but available upon request.]
Cheers!