Welcome to the forum.
Every monster that was released is still available, either in an egg, in the shop or in the friend chest. The hardest monsters to get are probably the friend chest exclusive monsters (they were usually reward monsters before).
New monsters that are not featured are given as event rewards and later been put into eggs, chests or the shop.
This complies to the gatcha laws in many countries.
Exclusive content are probably only icons that are not available to new players, like anniversary icons or such content. There is also no way of obtaining all icons, often you have to choose one icon of two or three, so nobody has all icons. This exclusive content is not relevant for the gameplay itself.
Every banner has a list where you can see which monsters are obtainable in that banner and how many % chance of getting them. The featured monsters are just higher percentage. Older monsters will probably be featured less often once they are put into the standard pool.
Other eggs, like rare gem or gold egg, also got a list and featured only monsters are usually getting updated into that list once a year around the anniversary.
Some shop monsters are stated as ‘shop only’, they can only be purchased there. Other monsters like Ankudragon are featured in banner before and now they are only available on welcome banner or in the shop. Monsters like the moth were reward monsters before and now probably shop only too.
At the top left, you can see the text ‘list of monsters’.
Inside that list, you can see which monsters are obtainable and the percentage. You can see, that the featured monsters are higher chance to get.