In a sentence with a main clause and a subordinate clause that takes place before the main clause, you must use the subjonctif passé:

Il faut que tu aies fini tes devoirs avant te sortir.

If the main clause is already in a past tense, so you must use the subjonctif plus-que-parfait:

Il fallait que tu eusses fini tes devoirs avant de sortir.

Nowadays the subjonctif passé is often used instead:

Il fallait que tu aies fini tes devoirs avant de sortir.

As Simon said, subjonctif imparfait is almost never used now, so in order for my own sentences to sound familiar I’ll use subjonctif présent.

Basically, there is a construction in French that goes :

Il n’y a rien que [subjonctif]

Here are some examples :

Il n’y a rien que je puisse faire.

N’y a-t-il personne ici qui sache comment faire ?

Il n’y a pas grand chose qui soit capable de le faire réagir.

1. It is possible only with negative sentences (rien, personne, presque pas,…) so you can’t use that tense with "Il y en avait beaucoup". I think the correct one is "Il y en avait beaucoup que je ne lui avais (pas) vu inventer". I’m not 100% sure though, it’s not a tense I use a lot.

2. See above.

3. According to this thread, it isn’t grammatical to use indicative here. In colloquial langage you might hear it but it’s a mistake.

Ex: "Nothing can stop me"

Il n’y a rien qui puisse m’arrêter

Correct, but very formal

Il n’y a rien qui peut m’arrêter

Not correct but can be heard. Colloquial.

Rien ne peut m’arrêter

Correct, less formal than the first one, but not as colloquial as the second.

I found other used of this construction in popular phrases :

Il y a pas de "mais" qui tienne !

When a parent is scolding their child and they respond, for example. "Mais" can be replaced with anything, the phrase means it’s not receivable, you’re not in place to say "but…" or ask for the thing.

Il n’y a que Maille qui m’aille

Slogan of the mustard brand "Maille". "Only Maille can satisfy me".