While GraemeDice is correct, there are a few ways you can try to get around most of your issues. Some of them however there is just no cure.
Before I get started though I'm going to sideline myself for a moment.
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There are pretenders that increase luck
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Do you mean they actually increase luck, or do you jsut mean fortune telling? Fortune telling only prevents bad events and doesn't do anything to make good events happen more often. And I can't think of any pretender that actually increases the chance for lucky events to happen.
Okay, so here are some potential work arounds to your problems:
1)Hero chance. There are only two things I can think of that would help here. First, make sure every hero slot is filled. I'm pretty sure it won't cause you to get hero events more often, but having lots of hero slots will at least prevent you from running out of heroes. Of course, having any multi hero would do that as well. The second, is to make luck a very attractive scale for the nation. You can do that a number of ways. By giving them absolutely horrible PD at low levels, so they need over 12+ to stop barbarian raids and call of the winds has a significant chance of success at low levels. Another option is to make them a high resource, very low gold cost nation. You don't need much gold so you can therefore take turmoil, which blends well with luck, thereby causing you to receive more heroes on average. Another way to entice players to use turmoil luck would be to give the mages lots of paths with good chances (or maybe bad chances, hmm, not 100% sure about this one) of being able to remotely site search in them, but giving them an almost completely useless starting gem income. Say, for example, letting the elves get all elemental paths, nature, and maybe astral, but their starting income is all in one path. While doing this though you have to keep them from getting too many random paths on one guy or it's too tempting to search manually instead. If you can think of any other ways to encourage the use of turmoil+luck that you think would work better, feel free to go there instead. But I do think encouraging turmoil+luck would be your best option.
2)Multihero randoms. This one is just not possible. The best you can do here is just to make their random paths very, very random. A hypothetical multihero could have 100% AWEFSN, 50% AWEF, 50%AWEF, 50%AWEFSN. There's still the chance that the randoms will add up, but it's pretty unlikely that you'd end up with a hero with more than 2 in any given path with randoms like that.
3) Differentiation between units of different houses. You'll have to be a little more clear on how you want to handle them. I mean, one could be armed better offensively and the other more for defense. One could favor light, faster units with low encumbrance and the other heavier, slower units with lots of armor. One could be better at ranged combat but have lower precision. They could have different mages and commanders associated with them. Especially if one house had stealthy units that could benefit from a stealthy leader. You could try to distinguish themselves from each other visually through their color scheme.... I'm unfortunately not too familiar with the specific lore offhand, so I can't make good appropriate suggestions for you right now. Hopefully I have at least sparked an idea.
4) Magic site autospawning. Again, this is not really possible, but you can use a workaround. Gandalf's mention of a magic site that you can enter to summon the creatures was a good idea, but I'm pretty sure it's not actually possible. There is no mod command that can allow you to summon creatures from a site in that fashion to my knowledge. I guess if you went and modded a unit that's summoned by a pre-existing site you could summon them that way, but I can't think of any site you could do that with that would be disruptive. Perhaps the one that lets you summon mummies? Anyway, instead of going that route, how about a magic site that lets you summon an immobile, unique commander unit that autosummons, domsummons, or makemonsters the birds? I think that is probably your best bet.
5) Earendil and his ship. I read the wikipedia article for him, then read the article for Ancalagon... again, I've not actually read the silmarillion. I'd go ahead and give him flying, and sailing, but leave out the size 6 trampling. It seems a bit... odd, to trample soldiers with a boat. I'd give him either innate reinvigoration, or encumbrance 0 to reflect his fighting the dragon for a day and emerging victorious, also I would give him an innate larger being-slaying weapon. I would go with the title "The Mariner".
By the way, that link leads to a Space Empires 4 post.