Rubber Specifications

1st
On semi pro and pro level this matters a lot. Not so much at amateur's level though.
Reason is that when hitting hard a thinner rubber bottoms out easier and sooner than a thicker rubber would do, which would let you feel the wood (blade) sooner. This would limit the amount of spin that can be imparted and hence thicker rubbers allow to hit harder plus put more spin on the ball.

2nd
Not sure if i got what you mean, but degrees aren't referring to rubbers as such but rather to sponge hardnesses. So like in the first answer, a softer rubber with a lower hardness degree which is easier to use for beginners would also bottom out much sooner and hence can't produce as much spin and speed as a harder rubber with a higher number of sponge degree would do.

3rd
Tacky rubbers (just like any other rubbers) have advantages and disadvantages.

The pros are at serving, serve receiving and the shortgame.

The cons are that you really have to work to hit with the same power like with a tensioned non tacky rubber. Hence you need good footwork to be in place to spin hard, 'cause the tacky rubber doesn't let you get away with lazy footwork and sloppy shots or not as much as a softer, tensioned non tacky version would do.

Hence my preference for tacky rubbers 'cause good footwork development and clean shots are essential for a developing player IMHO.

To your last question: the numbers on the rubbers like the (24-057) you've mentioned are the ITTF registration numbers a tt-company needs to register a rubber at the ITTF for the LARC (list of approved racket coverings) to be able to be used at official competitive matches.
For unofficial hobby usage no registration and hence no number is needed.

Tackiness of rubbers has quite complicated effects.

In theory, everything else being the same, tackiness reduces both speed and spin. But e.g. allows giving extreme topspin in conditions where the ball would risk slipping off a non-tacky rubber. (See this blog post for a detailed explanation: https://thoughtsontabletennis.wordpress.com/2015/08/20/on-tacky-rubbers/)

In practice, popular tacky rubbers differ from popular non-tacky rubbers in many more ways than just tackiness: tacky rubbers tend to have harder sponges, shorter pimples + thicker flat rubber outer sheet; tacky rubbers also tend to perform best when used with boosters; price (commercial h3 neo can be found for less than 1/3 of the price of tenergy). One of the common use for hard tacky rubbers is as a forehand rubber for technical, high tempo, close to the table topspin game looking to take the offensive with aggressive topspin as early as possible (3rd ball). Because tacky rubbers tend to be terrible for flat hitting, and yield high rewards for good looping technique, some people also favor them for learning the latter.