"Plus" is always an adverb, no matter what source : "plus" from Larousse dictonary.

In French, "Plus de" has a lot of meaning, it can be "no more"

Je n’ai plus d’argent. I don’t have money anymore

or used to compare

J’ai plus d’idées que toi. I have more ideas than you

Tu a plus de pommes que moi. You have more apples than I

Ils ont plus de temps que nous. They have more time than us

"Plus de" is used to compare "Je" and "Toi", meaning that "Je" got more ideas than "Toi". "Idées" is on the plural because there is more than one "Idée"

On your second question, yes you can use "plus de"

Je suis un étudiant pauvre. Je veux plus d’argent. I’m a poor student. I want more money

J’aimerais plus de temps. I would like to have more time

Tu peux m’en passer plus ? Can you give me some more?

According to the Trésor de la langue française (plus, I A 2 c), the structure plus de + noun is to be considered an adjective (adjectif indéfini).

According to the Bon usage (14^e édition, 2007, §626a), it is a déterminant indéfini, which is basically the same thing as an indefinite adjective, but through a slight change in grammatical conception that resulted in the name change observed (the earlier editions used adjectif indéfini).

§626 states:

Adverbes de degré comme déterminant indéfinis.

[…] Followed by de and a noun, the adverbs of quantity are equivalent to indefinite determiner. They do not vary and have meanings along the lines of their meanings as adverbs.

Therefore, plus d’ in your example “J’ai plus d’idées que toi” is indeed not an adverb, though it behaves somewhat like one, since it doesn’t vary.

How you are learning to call it, indefinite adjectives or indefinite determiners, should not be of huge consequence at this point in your learning, and I would suggest you stick to your references’ terminology in order not to get confused.

Followed by a noun, I can think of no examples where you would be allowed to drop de in between plus and the noun, statement for which I’ll except an informal familiar register statements where the noun itself is used almost as an adjective:

Maintenant, ça fait plus cuisine.

• Now it is more (like a) kitchen.

So it will have to be:

I want more money:

• Je veux plus d’argent

I got more ideas for the project:

• J’ai eu plus d’idées pour le projet

More models are out:

• Plus de modèles sont (maintenant) disponibles