Mounts are useful out of combat for traveling long distances and carry lots of gear without the character ranking up exhaustion points.
In combat a mount can have some usefulness but the standard mounts are rather vulnerable. Effectively speaking a controlled mount is a buff to a player characters mobility, enabling the character to travel larger distances. ...
Technically speaking, no.
Mounted is a specific situation, and you don't count as mounted unless you are actually mounted or have a special ability that says you count as mounted.
A DM might decide to allow this.
However, if they do, the lance becomes by far the best weapon for a centaur. It has weaknesses (in the disadvantage for fighting within 5 feet), ...
A creature is only considered mounted if it is riding something
The rules for mounted combat (Player's Handbook, p. 198) say:
A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount, using the following rules.
So, the centaur is not considered mounted if it isn't riding something. His racial ...
The Complete Paladin's Handbook by Rick Swan provides the information you seek. Some example exotic mounts are: unicorns, pegasi, griffons, giant eagles, elephants, lions, tigers, dire wolves, hippocampi, dolphins. There are also others; and DM's choice is also left out as an open-ended option. The book also recommends establishing rules for such exotic ...
Pointing out to the OP, considering the assumption that he is playing a Paladin with a summoned mount:
Page 198 PHB
Controlling a mount ... Intelligent creatures, such as dragons, act
independently. ... An independent mount retains its place in the
initiative order. Bearing a rider puts no restrictions on the actions
the mount can take, and it ...