[RPG] Circle of the Moon druid CR discrepancy for Wild Shape on D&D Beyond

Elemental Wild Shape just grants access to different forms for you to Wild Shape into. As such, it's limited by all the restrictions and gains all the benefits of normal Wild Shape.

To answer the second half of this question, we need to know if Beast is a keyword, or if it's simply a general descriptor that could apply to anything we Wild Shape into. The answer to this is that yes, Beast is a keyword monster descriptor.

However, that is thankfully irrelevant. The text under Beast Spells refers primarily to Wild Shape, and has ancillary text that refers to Beast Shape. However, based on the text in Wild Shape, I believe that they are used in the text interchangeably and thus should be applied interchangeably for the rare case where you are not in a Beast form.

So yes, you can cast spells while an elemental using Beast Spell.

There are no rules that state that a wild shaped druid is not able to take or benefit from a short rest. There is a clearly defined list of what they cannot do in the PHB.

As there is no requirement to maintain concentration or focus on the shape, and because transforming does not break concentration on existing spells, a druid is able to meet the requirements for a short rest.

PHB Page 67
You retain the benefit of any features from your class, race or other source, and can use them if the new form is physically capable of doing so.

PHB Page 186
A short rest is a period of downtime, at least 1 hour long, where the character does nothing more strenuous than eating, drinking, reading or tending to wounds.

Unless your form is described as a never stopping ball of energy, most forms are capable of resting, and therefore are capable of regaining uses of wild shape.