You seem to be right about parallel construction as practiced by the DEA/NSA. That revelation came out in a Reuters' report in 2013 rather than from the Snowden leaks.
Regarding gag orders, I'm referring to National Security Letters. Google, Yahoo, Twitter, etc. all received them with corresponding gag orders.
The NSA's documents when referring to the collection on those unencrypted fiber lines use the terms “full take,” “bulk access” and “high volume”. Perhaps they do not duplicate and store everything, but they certainly have access to everything, which is not much better.
You can read more about Bullrun on Wikipedia. It seems there is much known definitively about it, and it's the source of the statement I made almost verbatim.
You may not find some of the content of the leaks surprising, but many do, and I was treated like a conspiracy nut for years and years for even broaching the subject. The extent of the coordination with foreign intelligence agencies, while also not surprising to me, is highly significant because it presents an obvious loophole to the whole "we don't spy on American citizens" with the unspoken addendum being "(but our allies do, and we can access that data whenever)".
Maybe you and I have pretty different notions about what is acceptable in terms of "intelligence" gathering. I believe that all spying, whether on Americans or foreigners, is wrong. I want to see the NSA, CIA, DIA, and organizations like them splintered into a thousand pieces and scattered to the winds, to borrow a phrase.