Let’s look at important things here –
Mercury - Mercury represents communication skills, marketing, calculative ability, younger siblings, hobbies, skills with hands, intelligence, quick decision making, logical thinking, youthfulness etc.
Ardra - Ardra is nakshatra of transformation, turmoils and chaotic events. This can be most closely related with accidents and emergencies. For more information on Ardra, please check this link - https://www.astrosaxena.com/ardranaksh.
Gemini - As Ardra is part of Gemini, Gemini sign and its representations become important here. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Mrigshira/Gemini.
Rahu - As Ardra is ruled by Rahu, Rahu's position and dignity will also have an important role in functioning and results of any planet in Ardra.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Mercury in Ardra Nakshatra – First of all, Mercury is in own sign. Hence, at sign level, Mercury is in good dignity. At the same time, as Ardra is ruled by Rahu, the malefic impact of Rahu will be on Mercury. As Mercury is all about communication and Ardra is all about turmoils and chaotic events, these people can become counselors to people who are going through turmoils in their lives. Now, to counsel someone in such matters, it is necessary that person should have some experience of same turmoil. So, this position can also bring turmoil in person's own life especially if Mercury is a relationship oriented planet for him. It can also make someone communicate about chaotic events. So, it can easily make someone reporter of crimes and investigations. As weapons and violence is part of story of Ardra, they can easily be Arms dealers etc. Positively, they can be interested in learning many different foreign languages which includes computer and technical languages too. They can be very well be in travelling related work, especially foreign travels. As Ardra is also closely related to health care, especially mental health care, these people can be good psychologists too.
Role of Mercury – As we are trying to interpret Mercury only, we need not to check position of Mercury separately.
Role of Rahu - Rahu's placement is important to guide Mercury in right direction as it is Ardra's lord.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Mercury in Ardra. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Mercury in Ardra can work in a chart.
Hope this helps. Please post any comment or query you may have.