Extremely strict internally. I remember reading somewhere that some Space Marine Chapters will have 1 hour of 'free time' a day in between training and other duties. For a Sisterhood that 'free time' would likely be spent in further prayer or reflection.
Could there be an order that, like the space wolves or the blood angels chapters for the astartes, differs from the standard order?
Certainly, this is simply a matter of remoteness and contact with other Ecclesiarchy authorities. A large Order based on or next to a major Shrine World would almost certainly adhere strictly to the standard doctrine of
SoB Orders. A much more removed Order, say one dedicated primarily to the protection of a single significant Shrine on a rather remote world (such as some long forgotten battlefield where a particular Saint or Imperial hero met their end), would eventually experience significantly more deviation from the standard. They may find themselves more 'community-minded' to the local faithful populace with charity mission or regular assistance on religious holidays. This would likely lead to some minor adaptions of their own faith assimilating local customs and beleifs, especially if they were recruiting locallyin addition to Schola Progenium candidates. Alternatively they might be more secluded than ever, time and habit making it possible that they develop their own quirky rituals and practices.
Which order is more important for a sister: one from an imperial authority (inquisitor/magos/ecclesiarchy member) or one from a sister of the order superior to the first sister but inferior to the imperial authority?
Technically an Inquisitor but at the end of the day, it comes down to who can smear the other with the taint of heresy first. A popular and well-respected Cardinal might successfully convince an Order's Canoness that this particular inquisitor is a radical and heretically tainted. 9 times out of 10 though, it's likely going to be the absolute authority of the Inquisitor that carries the most weight. Certainly so if their own integrity or faithfulness is unassailable by their detractors.
An individual sister, if forced to choose immediately on the battlefield between the order of an Inquisitor and the order of a Canoness, would likely follow her Canoness. If an Inquisitor barged into a convent and declared the Canoness was a heretic it is likely that the Order would rally to her defence unless they had their own reason to suspect something.
The reason Inquisitors don't use Sisters more regularly as their own personal army is threefold.
1) They're something of a blunt instrument. Zealotry and unsubtle tactics don't lend themselves to delicate investigations. Stormtroopers can be kept on hand for that.
2) There are some orders or directions that a Sister simply will not obey with the same stubbornness of a Space Marine. This might include refusing to abandon a shrine in the face of an overwhelming enemy force or taking a heretic alive rather than blamming them on the spot.
3) If the Sororitas suspected even for a moment that the Inquisitor they were working for was dabbling in some of the more questionable practices of a Radical, they would be the first to ENGAGE PURGEMODE. In fact, aside from some more zealous Space Marine chapters, they'd likely be the only Imperium military force that would do so on the spot without hesitation.
To become a sister repentia, what kind of sin is committed by the sisters to not be shot on the spot like usual heretics?
Fairly minor sins, such as a failure or moment of weakness of some kind. Impure thoughts or a lack of conviction. Most of the time I think they actually volunteer themselves, Sisters are generally highly critical of their own failings and base human limitations. Probably a Catholic thing.
For example, refusing to purge a defenceless town of potential heretics would likely get a sister executed. Merely carrying out the purge without enough enthusiasm might get them placed in the Repentia.
