Is there a comma splice AND is this a restrictive or nonrestrictive clause?

First of all, a warning: your sentence

*My Professor, who was essential, so I spent as much time as possible in her office.

is not acceptable English (the asterisk '*' in front signifies that what follows is not an acceptable English sentence). It is not acceptable for the same reason the following is not acceptable:

*My Professor, so I spent as much time as possible in her office.

Presumably, you wanted to say something like this instead:

My Professor, who was essential, let me spend as much time as possible in her office.

First example

The example

[1] My professor was essential, so I spent as much time in her office as possible, hoping that she would guide me through the subject.

has nothing to do with restrictiveness. As DW256 pointed out in the comments, the question of whether something is restrictive or not really only arises for relative clauses.

In [1],

[2] hoping that she would guide me through the subject

is a supplement. The 'non-restrictive relative clauses' you have in mind are also supplements, but [2] is a different sort of supplement.

In general, a supplement is a word or a word group that is not syntactically integrated with the rest of the sentence. Instead, it bears a purely semantic relation to some part (called the anchor) of the main sentence. The supplementation can be marked in various ways: by commas, dashes, parentheses, or (for appendages in end position) a colon (CGEL, p. 1350).

The supplement in [1] has the form of a non-finite clause (in particular, a gerund-participial clause).

The anchor of [2] in [1] is the clause I spent as much time in her office as possible.

(Incidentally, as far as I know, the question of whether a construction is restrictive or not can only arise when the anchor is a noun phrase—like in your second example, which we discuss below.)

In your case, the supplementation could be marked in any of the following ways:

My professor was essential, so I spent as much time in her office as possible, hoping that she would guide me through the subject.
My professor was essential, so I spent as much time in her office as possible (hoping that she would guide me through the subject).
My professor was essential, so I spent as much time in her office as possible—hoping that she would guide me through the subject.

A colon, however, would not work in this case.

User MarcInManhattan has suggested that it could be useful to contrast the following two sentences:

[3]  i  I spent time in her office hoping that she would guide me.
       ii  I spent time in her office, hoping that she would guide me.

In [3i], hoping that she would guide me is integrated in the syntactical structure of the sentence; it is a modifier in clause structure. In [3ii] it is not integrated, so it's rather a supplement.

There is a subtle difference in meaning between [3i] and [3ii]. [3i] implies that what the narrator was doing while in her office was hoping that she would guide him. In contrast, [3ii] does not imply this. Instead, [3ii] would most naturally be interpreted as saying that the reason the narrator spent time in her office was that he was hoping she would guide him.

Second example

In the sentence

[4] My Professor, who was essential, let me spend as much time as possible in her office.

the part in boldface (who was essential) is again a supplement. The form of this supplement is that of a relative clause, which is a particular type of subordinate clause. (Subordinate clauses may be integrated, or may be supplements.) This really is an example of a 'non-restrictive relative clause', i.e. a relative clause that is semantically non-restrictive.

The anchor of this supplement is the noun phrase (NP) my professor.

Again, there are at least three ways this supplementation could be marked:

My Professor, who was essential, let me spend as much time as possible in her office.
My Professor—who was essential— let me spend as much time as possible in her office.
My Professor (who was essential) let me spend as much time as possible in her office.

So, a'non-restrictive relative clause' is a particular example of a supplement. Such a clause is semantically non-restrictive precisely because it is not integrated in the syntactic structure of the sentence. Only an integrated construction can be semantically restrictive.

The converse, by the way, is not quite true. In other words, it is not true that an integrated construction must be semantically restrictive, though it very often is. Here is an example. The boldfaced part in the following sentence is a relative clause that is integrated into the syntactical structure of the sentence. Nevertheless, it is not semantically restrictive.

[5] The father who had planned my life to the point of my unsought arrival in Brighton took it for granted that in the last three weeks of his legal guardianship I would still act as he directed.

As CGEL (p. 1353) says,

The relative clause doesn't distinguish one father from another: the narrator has only one father, so the modifier provides non-restrictive information about him.