-What is a Thane?
A Thane is one 'rank' below vassal, as a Thane you are oath-bound to serve your Jarl, Count, Noyan or whatever just like that Jarl, Count etc is bound to serve his king / khan. A Thane could be another (skipable) step to go through before vassalship.
-What is a Thane's duties?
A Thane, as said is oath-bound to serve his Liege as good as he can, assisting in raids, defending from threats, etc. Most, if not all actions carried out by a Thane will be considered as the will of that Thane's Liege. Which means that a Thane could raid a (friendly) village, attack a (friendly) lord or cause similar mayhem at the Liege's cost. (you will not be held responsible, at all, no minuses or bonuses such as honour, relation changes or similar.) Of course, the lord can dismiss, capture or even banish a Thane on behalf of the faction if caught doing such. At that point, you will suffer losses of relationships, honour and similar. Not good.
-Can I have my own Thane as a lord?
Yes, you can always promote of your companions to your own personal Thane, noble companions are unlikely to accept this offer, as their ambitions aim higher. After a long service as a Thane, promoting that (unnoble) companion to a lord will not be considered inappropriate among other lords.
You can find disbanded Thanes at taverns too, looking for a new lord. This is rare, however. They can be expensive, and judging from that individual Thane, not consider you worthy of his service. Depends on renown and honour. You can have a maximum of 3 Thanes in your service. You must have status as a lord or higher in order to have any Thanes.
-How will my Thanes behave?
Your Thane will not stay in you party anymore, and will upon recruitment/promotion leave you and set out to recruit troops, faction type depends according to your fancy. A Thane will hire between 20 and 50 troops. When finished, you will receive word about it, and your Thane will now always accompany you, assist you in battles (no matter the odds), and take general orders such as raiding villages. A Thane does not mind following you around, no matter how long you keep them doing it. A Thane will always have 0.1 faster travelling speed than you have.
Thanes demands payment depending on how many troops they have and what they have done for you this week.