Credits to ICE for writing this

Options explained. From top to bottom:

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Home
Select a sector or an object
Here is what your captain will consiter their home. Choose carefully, depending on what you've chosen here - your captain's idle behavior will also chance. Details below.

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Destination
Select a sector position
Can be blank. It's only used in certain idle cases. Details below.

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Dock, hold, Def, Patrol
Select a number from 1 to 4 where 1 is 'Dock' and 4 is 'Patrol'
Here is what your captain is supposed to do while not busy responding to distress calls. Depending on what you've selected as ship's home some options may behave differently:
If your home is a sector:
- Dock:
You obviously cannot dock into a sector, so your captain will move to posion, you've selected as "Destination" and hold.
- Hold:
The same as above.
- Def:
You captain will do the very same thing, as if you've issued the vanilla "Defend position" order. The only difference here is that they will respond to distress calls within given parameters.
- Patrol:
You captain will do the very same thing, as if you've issued the vanilla "Patrol" order. The only difference here is that they will respond to distress calls within given parameters.
If your home is not a sector:
- Dock:
If your captain can dock into Home - they will. If they can't, they will just move to home's position and hold.
- Hold:
Your captain will hold position near Home.
- Def:
Your captain will Defend it's Home, whatever it is.
- Patrol:
You captain will do the very same thing, as if you've issued the vanilla "Patrol" order. The only difference here is that they will respond to distress calls within given parameters.

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Assign as home base
Yes or no
If set to Yes and your 'home' is a player owned object - your captain will become it's subordinate.
Yes, it can be another Reaction force's ship.
Yes, both will act independently only following each their own settings, so you can set a carrier to only respond to large ships and a carrier's subordinate to respond to smaller ships and they will work just as you would expect.

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Response Range
Range in sectors
Set the range in sectors from home to a ship in distress, that your captain is supposed to respond to. Zero means that they will only respond to calls from within their home sector.

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Allowed threat level
Choose a number from 0 to 20
I know it's horribly worded. I will probably change the option's name later.
0 means that your captain will completely ignore threat assesment and will respond even if they're piloting an S class interceptor and an enemy has a 100 ships fleet. Suicidal.
1-4 means a predicted loss. Your captain will respond even if their assigned fleet is weaker then the enemy. 1 is more suicidal then 4.
5 means an uncertain outcome. If your captain's fleet roughly is equal to an attacker's fleet - they will respond.
6-20 means that your captain will only respond if the upcoming fight is a predicted win. 6 is more dangerous then 20. In less abstract numbers:
6 means your fleet should be 10% stronger then enemie's
20 means your fleet should be 150% stronger then enemie's
Please note that prediction is rather accurate, but only for out of sector (player is not nearby) battles.

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Respond to ships
Choose yes or no
Whether your captain should respond to a ship in distress.

HP%
Choose a % of damage
Choose how badly damaged should a ship be for your captain to decide to respond. Yes, shields do count.
100% means that the ship got shot at. Maybe even wasn't scratched. The response will come.

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Respond to C ships
Choose yes or no
Whether your captain should respond to a COMBAT ship in distress. Very useful to avoid unnecessary 'help' when you're fighting within your reaction force's area of operation.

HP%
Choose a % of damage
Choose how badly damaged should a ship be for your captain to decide to respond. Yes, shields do count.
100% means that the ship got shot at. Maybe even wasn't scratched. The response will come.
I do recommend keeping it below 100%. Maybe 70, just like the default.

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Respond to stations
Choose yes or no
Whether your captain should respond to a station in distress.

HP%
Choose a % of damage
Choose how badly damaged should a ship be for your captain to decide to respond. Yes, shields do count.
100% means that the ship got shot at. Maybe even wasn't scratched. The response will come.

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Respond to player
Choose yes or no
Whether your captain should respond to distress calls from a player owned objects.

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Respond to Distress
Choose yes or no
Whether your captain should respond to distress calls from an ally owned objects.

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Silent notifications
Choose yes or no
Do not BEEP when a response is sent.

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Attack S
Choose yes or no
Whether your captain should respond if the attacker is piloting an S class ship. If set to false and there are only S-class ships in the attacker's fleet, the call will be ignored.

Attack M
Choose yes or no
Whether your captain should respond if the attacker is piloting an M class ship. If set to false and there are only M-class ships in the attacker's fleet, the call will be ignored.

Attack L
Choose yes or no
Whether your captain should respond if the attacker is piloting an L class ship. If set to false and there are L-class ships in the attacker's fleet, the call will be ignored.

Attack XL
Choose yes or no
Whether your captain should respond if the attacker is piloting an XL class ship or an attacker happens to be an enemy station. If set to false and there are XL-class ships in the attacker's fleet, the call will be ignored.

In general - your captain will not respond if the attacker's fleet contains any ships that are bigger, then they are allowed to attack.