Character still walking when no key is already pressed

I have the following animation controller:

As you can see, there are 4 different walking animations and 4 corresponding idle animations.

There are also transition conditions between them:

 any state -> walkdown -- DirY < -0.1
 any state -> walkleft -- DirX < -0.1
 any state -> walkright -- DirX > 0.1
 any state -> walkup -- DirY > 0.1
 
 walkdown -> idledown -- DirY < 0.1 && DirY > -0.1
 walkleft -> idleleft -- DirX > -0.1 && DirX < 0.1
 walkright -> idleright -- DirX < 0.1
 walkup -> idleup -- DirY < 0.1

I also wrote the following code for the character animation:

 void FixedUpdate() {
     float xAxis = Input.GetAxisRaw("Horizontal");
     float yAxis = Input.GetAxisRaw("Vertical");

     GetComponent<Rigidbody2D>().velocity = new Vector2(xAxis, yAxis) * Speed;

     GetComponent<Animator>().SetFloat("DirX", xAxis);
     GetComponent<Animator>().SetFloat("DirY", yAxis);
 }

It works but I have the following questions:

• Is it the appropriate way to make transitions between such states? I mean, DirY < 0.1 && DirY > -0.1 and DirX > -0.1 && DirX < 0.1 looks quite rude but hey, is it ok?

• I noticed that sometimes the character still walking when no key is already pressed. I think that's because of the FixedUpdate method nature -- it is called every n milliseconds. Am I right? Is there any workaround to change animation immediately? I already unchecked the Has Exit Time checkbox in Inspector.