Mounted combat/Find Steed (5e)

Dear Fellows,

I am going to play my second DnD scenario as a Paladin and will take the Find Steed spell at lvl 2 [Edit: 5]. I therefore have question on mounted combat.

For what I have understood my Steed, when mounted, will have the same initiative as mine and will be able to use all his movement (e.g. 60 ft. for a Warhorse) and take an action such as dash, disengage or dodge, while I will be at the same time taking my turn and thus being able to attack, cast spell, etc.

Could anyone please confirm this and especially the fact that with a Warhorse having 60 ft. speed I can move 60 ft., use an action for attack and then disengage [Edit: dash]?

Also wouldn't making a U-Turn with a Warhorse harms RP?

Thank you very much for your help, have a nice day!