What would it mean to have been a Marshal of the szlachta in a district, and a judge, in the early to mid 19th Century?
That would be created by Russia an office that merged some of Polish nobles traditional autonomous system of government with centralist regime of Russia. I will post details later.
Marshal in Polish tradition and system was the title of the royal court official(nominated by the King) or court official(elected), or sometimes civil official (elected).
What would have been the role of a Marshal (Marszalek), how was it conferred on an individual, and what were the responsibilities and obligations associated with same?
I would say it was middleman between nobles and governor.However Marshal of Szlachta has been created after 1772 on the territory garbed by Russia.
You can find such office in the collection of laws of the Russian Empire 1842.
Marshal of Szlachta was deputy of Russian governor and was responsible for dealing with all autonomous bodies of Szlachta as well as collecting taxes.(they had their own office)
Marshals were taking part in the court cases if it involved complain against petty official. They were responsible for census in their county and were taking part in government commissions which were taken care of all issues imaginable from overseeing constructions to drafting men into army.
Also they were arbitrating all issues regarding nobles, like managing estates of minors, indebted estates and cases of owners especially cruel to their serfs.
What would it mean to have been a Marshal of the szlachta in a district, and a judge, in the early to mid 19th Century?
Marshal of szlachta was elected by all nobles in the county for three years. What judge? Are you sure you don't mean arbiter? A judge it those times could mean a number of things.
Was there any educational requirements, such as a University degree?
Well Polish nobles as a rule have been educated very well but I don't think that any formal education was prerequisite to that office.
Were there any military connotations in respect of being a Marshal?
Just paperwork for the military and dealing with draft.
Hope it will help you.