Any tips to increase my cavlary speed and check its details anywhere?

You can increase the speed of cavalry by doing research under "Cavalry training". It is called purebred steeds

When using all cavalry in your legion it will march the fastest. As well as the research mentioned already, to improve it further you can also craft parts in the Blacksmith building. Steel cavalry parts will improve stats when you are only using cavalry troops and the boots and ransur items will help improve your marching speed.