Hey, questions are good

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1. There is a paradigm of the future perfect indicative of λÏω. The future perfect middle is basically formed by adding -σομαι to the stem of the perfect middle. Reading Monro's grammar, he doesn't mention the active, so I guess it doesn't occur in Homer (and it's very rare in Attic Greek). Conjugation is like the normal future.
2. Yes, without the augment. The augment only occurs in the indicative. For ἀείδω, the aorist is ἤεισα so the unaugmented stem is ἀεισ- and the subjunctive is ἀείσω, ἀείσῃς, ἀείσῃ, etc. for ἕαδον the subjunctive would be ἅδω, ἅδῃς, ἅδῃ, etc. as you say.
3. Sometimes the subjunctive has extended endings, e.g. both λÏω and λÏωμι are possible, and so on.
4. You're right. Lots of the perfect forms are formed with participle plus the corresponding form of εἰμί.