Hey, questions are good
1. There is a paradigm of the future perfect indicative of Î»ÏÏ‰. The future perfect middle is basically formed by adding -ÏƒÎ¿Î¼Î±Î¹ 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 á¼€ÎµÎ¯Î´Ï‰, the aorist is á¼¤ÎµÎ¹ÏƒÎ± so the unaugmented stem is á¼€ÎµÎ¹Ïƒ- and the subjunctive is á¼€ÎµÎ¯ÏƒÏ‰, á¼€ÎµÎ¯Ïƒá¿ƒÏ‚, á¼€ÎµÎ¯Ïƒá¿ƒ, etc. for á¼•Î±Î´Î¿Î½ the subjunctive would be á¼…Î´Ï‰, á¼…Î´á¿ƒÏ‚, á¼…Î´á¿ƒ, etc. as you say.
3. Sometimes the subjunctive has extended endings, e.g. both Î»ÏÏ‰ and Î»ÏÏ‰Î¼Î¹ are possible, and so on.
4. You're right. Lots of the perfect forms are formed with participle plus the corresponding form of Îµá¼°Î¼Î¯.