Magnam partem illarum urbium post multos annos vi et consilio capiebat.
here magnam partem is Accusative, illarum urbium is dativ plural, multos annos ablative and what is vi? consilio ablative
translation must be
Multos annos is accusative.
vi is the ablative of vis vis, which means force, power;
It is lacking the subject, and translates more or less like that: (who?) captured a large part of those cities after many years by force and by sagacity/plans
Ipsi autem libertatem civium suorum magna cum cura aluerat.
they themselfs however freedom of their country with care support.
here civium is in accusative and magna in nominative, if magna is connected to civium, why it is not in accusative too? I don't understand
civium is dative plural of civis, civis, and mean citizen
magna is not connected to civium, rather, with the cum cura, it is a common construction to put the modifiyng adjective of the preposional object before the preposition. Examples: per varias regiones = varias per regiones; in cubiculo tuo = tuo in cubiculo
You forgot the verb in your tranlation: had maintained;
it is not of their country, but of their citizens;
And it is "with great care"; not care support