Verb て-form + もない meaning

Question

Example sentence, which is a response to someone who is talking like they were already invited to a party:

まだ誘ってもないのに｡

I'm not able to wrap my head around the grammar used in what looks like a pretty simple sentence:

1. Why is the verb in its conjunctive form?
2. What is the ない negating? Is it negating the verb 誘う, or is there a ある verb here that is being negated? Or something else entirely that I'm not seeing?
3. Is that the only location where the も particle could fit in naturally? Assuming it means something like "even" here.

Answer 1

You seem to have missed the -teiru form. Let's look at this step by step:

• 誘う: a transitive verb, "to invite (someone)"
• 誘っている: the -teiru form of 誘う to express the resultant state, "has invited"; See When is Vている the continuation of action and when is it the continuation of state?
• 誘っていない: negative form of 誘っている, "has not invited"
• 誘ってない: a colloquial version of 誘っていない "hasn't invited"; See: What is the difference between ～してる and ～している?
• 誘ってもない: added も meaning even, "has not even invited"
• 誘ってもないのに: added のに for regrettable feeling

So the entire sentence means:

まだ誘ってもないのに。
I haven't even invited you/them yet (but you/they are here)!

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Is that the only location where the も particle could fit in naturally? Assuming it means something like "even" here.

Another way to add も in this context would be 誘っていもしないのに, but this is much less common. For the grammar, you may find this interesting.