"The sky is blue" - Is it a clause?
Solution 1:
To answer your first question: blue is not an object in this sentence. It is a complement, more precisely a predicative complement. There are two sorts of predicative complements: subject-related predicative complement (also known as a subject complement) and object-related predicative complement (a.k.a. object complement).
Blue in your sentence is a subject complement. A subject complement follows a linking verb and gives more information about the subject by identifying or describing it. It can be a noun, pronoun or an adjective (or a noun phrase, or an adjective phrase...). When it is a noun or a pronoun (or a noun phrase) we talk about a predicate nominative. When it is an adjective we talk about a predicate adjective. This is what "blue" in the example is.
How do you know if something is a subject complement or an object in a sentence?
Only transitive verbs can have direct objects. So, check the dictionary definitions of the verb in your sentence (most dictionaries will state if the verb is transitive, intransitive or can be both).
Try to make a passive voice construction. The object becomes the subject in the passive. A (predicative) complement cannot become the subject of a passive clause.
An adjective cannot function as an object. Ever.
** We could dig deeper into this but I think we shouldn't because: a) it might confuse you and b) it might confuse me. So we'll leave it at that.
To answer your second question: It is a clause and a sentence. As Kathy said (and according to Longman English Grammar) a clause is
a group of words consisting of a subject + finite verb (+ complement or object if necessary).
A sentence can contain one or more clauses. If it contains one clause ("The sky is blue") it is a simple sentence. If it contains more clauses it can be a compound sentence or a complex sentence.