How do Christians justify worshiping someone who kills naive children/innocent beings?

Your question about Elisha and the curse called down upon his taunters in the name of YHWH has been fully answered by Korvin Starmast. With regard to the fig tree cursed by Jesus (Mark 11:12-14; 20-21) there is more to this than at first might be obvious.

This event took place at Passover, on the Monday of Passion Week. It was not the season for figs. Fig-trees around Jerusalem normally begin to get their leaves in March or April but do not produce figs till June. This particular fig tree was an exception to that natural rule in that it was already full of leaves at Passover. But it was not bearing any fruit. When a fig tree is full of leaves and fruit, the tree only has to be shaken for the figs to fall down (Nahum 3:12).

Why did Jesus curse the baren fig tree? Perhaps it was a parable of judgment on Israel (see Hosea chapter 9). This is a lesson to all who mock, scoff and ridicule YHWH and his anointed prohets (such as Elisha and Jesus). On the other hand, those who have faith in God and respect his appointed servants will experience God's blessings.

That is the lesson to be learned from the fig tree incident. Only an uneducated child would leap to judgment against YHWH and Jesus.

Source: New International Version Study Bible notes.

Reading the whole chapter in context tells a different story

Also remember that the Bible wasn't written in English. The presumption of "innocence" on the part of those taunting the prophet Elisha is at odds with the narrative as presented.

The prophet is speaking on God's behalf: this is serious business

As explained in some detail at this biblical study site, there are a number of messages being sent, some of which you are taking at face value in a modern English devoid of context.

Key Points for Understanding the Passage

In general, the OT is filled with examples (like Soddom and Gommorah) demonstrating that those outside the covenant with God often feel God's wrath

1. Your understanding of "young/youth" is influenced by an anachronism.

   Young men typically underwent their rites of passage into manhood in their teens in those days. A view of "young" and "youth" entitlement to be irresponsible is a modern anachronism that fails to match the cultural context of the passage. The "you are not an adult until you are 18/21" assumption is a modernity that isn't applicable to the Biblical narrative. (ON a related note, squires were going to battle at around age 14 in Europe during medieval times ...) If you overwrite "children" (pre pubescent boys and girls) into that passage for the term used, you are using deliberately the least charitable interpretation. As the author points out:

   The Hebrew word underlying what I have translated “juveniles” is notoriously difficult to translate in this context. The word can mean “child,” “servant,” “young man,” or several other possibilities, depending on the context. For example, it is used of the “young man” Absalom (1 Sam 18:5) and a group of 400 Amalekite warriors 1 Sam 30:17. The generally agreed meaning is that it is used of a young man (& can include females in the plural) who is not yet betrothed, setting the range from a mere boy to a young warrior. This passage uses the additional adjective “little” or “young” in the first case, which may tilt the meaning more towards the “children” end of the spectrum, but it’s certainly not clear. I’ve chosen the somewhat clunky “juveniles” to reflect this range, though the translation is admittedly less than ideal.

2. What was going on in this interaction?

   It is a challenge to the authority of God's prophet. To summarize the points made by Mr Staples:

   • Elisha wasn’t an old man; he was probably closer to the age of the older “children/juveniles/young men” in the group taunting him than to their parents.
   • The emphasis is that the youth of Bethel reject and scorn YHWH’s prophet (signaling a rejection of God himself). Rather than receiving the prophet, they tell him to “go up.”

   The exact word (עלה) used to describe Elijah’s departure to heaven twelve verses earlier. That is, they tell him to stay away, that they wanted nothing to do with him or his God, that he should go join Elijah in heaven if he was really such a powerful prophet

   {My note} This amounts to blasphemy in the context of the time. If you go back to OT times, blasphemy was often punishable by death.

   • Bethel is a city teeming with idolatry (Dan being the other), complete with a golden calf. A generation after Elisha, Amos cursed Amaziah, the priest of Bethel, declaring,

     “Thus says YHWH, ‘Your wife will become a who*e in the city, your sons and daughters will fall by the sword, your land will be divided up by a measuring line, and you yourself will die upon unclean soil'” (Amos 7:10–17).

   • Elisha’s curse takes a similar form to the curse for rejecting YHWH in the covenant from Sinai. YHWH doesn't take kindly to those who reject the covenant:

     “If then you act with hostility and are unwilling to hear/obey me … I will send the wild beasts among you and bereave you of your children” (Lev 26:22–23).

   • Elisha purified the accursed, polluted water of Jericho, bringing blessing to those who received YHWH in his first significant act as a prophet; this second act serves as a sign of God’s continued judgment upon covenant-breakers. {My Note} Note the underlying pattern here; the prophet can bring YHWH's blessing (first act) or his wrath/judgment (second act). This is crucial context to understanding what is going on in this chapter in the second book of Kings.

   • Now go back to the basics and view this as an illustration of the conflict between the covenant-keepers (Elisha's people) versus the idolaters/covenant breakers (those from Bethel). As with other examples, YHWH's judgment/displeasure was visited upon the idolaters and blasphemers.

3. The message is clear, and utterly consistent within the Old Testament context: God Will Not Be Mocked, So Don’t Taunt a Prophet of YHWH.

   It makes even more sense if you consider that these 'juveniles' have a far closer affiliation to gangs or mobs of teenagers (who in the OT context are already of age) than some vague notion of "innocent children" depicted in your question. (Some real life context: there was considerable violence initiated by teenaged gangs when I was going to high school in the 70's; teenaged males are often in a rebellious stage/mode, and this sometimes turns violent. The cops ended up at our high school more than once ... ).

Bottom Line

This answer challenges the frame of the question based on an example of biblical exegesis.

About that fig tree

The fig tree parable in Mark has a variety of interpretations, one of which you can read in detail here. This parable, similar to the account of Jesus controlling the winds on the Sea of Galilee, illustrates Jesus' divinely derived authority. In your question you attempt to read it as though it weren't a parable, or an allusion to larger things of which the fig tree is powerfully symbolic.

Once we recognize that the fig tree incident is recorded as a teaching situation, the lesson of which is given in the events and sayings of Jesus in the following verses, the reasons for Mark’s letting the reader know that Jesus was hungry (12), that he knew the distant fig tree was in leaf (13), and that it was not the season for figs (14), begin to come into focus. The fact that Jesus was hungry provides not only the immediate reason to approach the tree (a fact essential to the narrative — approaching a fruitless tree only to be disappointed would be meaningless unless someone was hungry), it is also vital to the prophetic declaration Jesus was to make. Many scholars agree that Jesus would have had in mind such passages as Jeremiah 8:13: "When I wanted to gather them, says the LORD, there are no grapes on the vine, nor figs on the fig tree; even the leaves are withered, and what I gave them has passed away from them." The fact that Jesus was hungry and approached the fig tree looking for fruit illustrates his identity and authority as the Judge of Israel who finds that the nation, despite its "leafy" appearance, has not produced the fruit God desired. (from the linked article)

This is another case reading the scripture outside of its context.

@Lesley provides a similar but not identical interpretation in the other answer.