Umka:
1. The probability of Logistics appearing is 15%(!). If, after a skillful summoning with Fire Warriors, you choose another skill, the probability of Logistics appearing further increases. Especially if you choose a popular skill, rather than one with a low probability. The hero will be at level 4 after the summoning. At what level do you encounter the enemy hero? Surely not before level 10? If not, then at level 8, you can already have Battle Mage and calmly acquire Logistics. Or you can take Wisdom with Attraction, and then Logistics at level 7. That's what I do. But on the other hand, you can also take Logistics (if you don't put 3 points into it in a row), and then other skills. You know best how successfully your hero clears out the neutrals and what he needs more: strength or speed.
2. I'll write more about breaking through mages in the thread about starting as the Elves.

Tell me, what is the map size, what hero do you have, and on what week does your battle with the Demon occur? With a Demon, after developing Logistics and Summoning, you can end up with no skills at all in battle (!), as the Imps will eat all the mana. You need to think about either developing Wisdom so that you have enough mana for at least a couple of spells, or developing troops so that spells become secondary.