1) No there is no cap on the number of players who can have their ELC slide.
2) Kozak is not eligible to have his ELC slide as he is too old. Players who sign at 19 (as of September 15 of the year of signing), but turn 20 before the end of that year are not eligible for an ELC slide.
3) Kozak is able to play in the AHL.
4) As far as the 50 contract limit goes, there are also no limits, at least in the CBA, on the number of players that a team can have signed that do not count against the limit.
5) The only signed players who do not count against the 50 contract limit are players who: a) are 18 or 19 [note: this is one area where the CBA is more vague than it should be, as player age is not defined in Article 1, and also is defined differently in different articles of the CBA], b) have been returned to juniors and c) have not played 11 NHL games in one season.
6) Per point a) above and its vagueries, it is not 100% clear whether Kozak would be exempt from the 50 contract limit if he were returned to juniors. However, my personal interpretation is that he would not be, as the exemption rules seem to refer to the ELC slide, which does not apply to players of Kozak's age.
7) As a larger point, as the CBA is written at least, the only players under contract who do not count against the 50 contract limit are those who have been returned to juniors (which is a term that is defined in Article 1 of the CBA, and specifically refers to the CHL). As such, any players who would otherwise not count against the 50 contract limit do in fact count if they are playing in Europe, or in the AHL. Along the same lines, a slide eligible player who is playing in the NHL counts against the 50 contract limit unless or until he has been returned to Juniors (provided he has not played 11 or more NHL games in that, or the previous, season).
8) Regarding the proceeding point, however, I would note that the strict text of the CBA does not always reflect how it works in practice. There are numerous points in the CBA where the wording is somewhat vague, and others where the text of the CBA seems to be disregarded altogether (such as the LTIR rules). It is possible, therefore, that players could be exempt from the 50 contract limit even if they play in Europe (CapFriendly seems to think so at least), although I would be very surprised if the same were the case for anyone playing in the AHL (whom CapFriendly also seems to think can be exempt).
9) That said, per the CBA itself, anyone playing in the AHL or Europe, while party to an NHL SPC, counts against the 50 contract limit, even if they would otherwise be exempt, and even if they are eligible to have their ELC slide.