The events of 2013-2014 that solely aimed overthrowing Erdogan were undeniably controlled by Gulen movement. However they lost the battle big time.

One or two weeks before the coup, some army officials in Izmir were detained linked with a previous army spy case and they were linked to Gulen. The supreme military council was about to be happening with the agenda of sacking multiple army officials related with him.

IMO, coup was not solely planned by Gulen, but they were involved significantly.

Lastly, again, check multiple coup officials' statements.

The confessions of a few captives, under duress from a dictator that's purging both public and private sectors of all opposition under false pretenses and threatening to bring back executions, carry very little weight in my book. There's a long history of compelled false confessions in similar circumstances.

The 2013-2014 protests consisted of just about everyone who opposed Erdogan.

Events of end of 2013 and 2014 were not about Gezi protests. This is about the corruption scandal and claims. Wikipedia link (Although probably quite biased) :

https://en.wikipedia.org/wiki/2013_corruption_scandal_in_Tur...

If you mean investigating the corrupt for corruption then I'd say that was closer to legitimate democracy than a coup.

it was their previous try. It probably contained legitimate claims mixed with stuff that fit their agenda. Now hopeless, they tried their last chance and failed miserably.