I would say the proper way to check to see if the towed is straight is to see if the baffles of the towed are completely opposite of your ownship course line/marker thing on the waterfall display. Note that on a mission with current enabled, you could be a significantly long time away from completing a turn (as in, it should be straight) but your towed will be forever bent to one way or another because the current is pushing it.
I usually don't fully deploy the towed because after a certain point, I see no discernible improvement in towed performance. A fully deployed towed at low speeds just means it takes longer to straighten out after a turn and longer to reel in if things start getting dicey.
The Akula lists the length of towed deployed on the conn screen and I believe the Akula one caps out at around 300 meters? Can't remember for sure, but approx. three boat lengths.
And to actually answer one of your questions (lol) The time it takes for the towed to straighten depends on both speed and the amount of towed deployed. Going slower = takes longer, more towed deployed = takes longer.
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