Wikipedia's article on Molodi, unfortunately, like many other articles on lesser known subjects, is a mess of random facts, confusing timelines and outdated information. It heavily mixes different events as a single entity, and I will try to clear things up a bit in explanation down below.

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Let's start with the question regarding fortifications.

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The article also mentions "innovative fortifications" used by the Russians. Is this referring to war wagons?

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This part in the article is worded in such a way that makes it look like Russians, predicting that the enemy would face them in this exact location, deployed some kind of new defensive mechanisms right before the action commenced, and managed to catch Tatars offguard. This is untrue; and phrase "innovative fortifications" should actually refer to a series of simple, but sturdy wooden palisades and earth moats dug up along the river of Oka between towns of Kaluga and Kolomna. Construction began in spring of 1572 and ended long before main bulk of Tatar army entered Russian territory; it resulted in reliable defensive perimeter roughly 250 kilometers long. Of course, it wasn't one single unbreakable line of castle walls and towers, since it was physically impossible to build it that way. These fortifications were actually more akin to guarding outposts, overlooking convenient river crossings and forest roads - i. e. paths an invading army was most likely to travel. Their purpose was not to help Russians during the possible general engagement, but to keep Tatar movements in check, spot them in time and redirect them to the grounds favourable for Russian side. Garrison along the newly formed protective line was reinforced in order to make it possible to pin down attacking forces long enough for the main Russian army to catch up with the invaders. These construction measures were also coupled with widespread torching of steppe fields located to the south of Russian border in late 1571: being deprived of supplies for their horses, Tatars would have to severely limit number of possible routes for their forces, and that made it easier to predict their possible movement.

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In other words, these fortifications weren't actually innovative, and it wasn't entirely about fortifications. Russian leadership took Crimean menace very seriously this time, and tsar Ivan and his subordinates employed active measures in strengthening both Russian defences and reconnaissance.

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By the way, there were actually no janissaries in Crimean army, contrary to what the article says. It mixes up Ottoman janissaries and Crimean "капыкулу" (khapiqulu) arquebusiers. Khapiqulu were indeed organized after janissaries and were to some extent their direct counterpart (elite corps of gunpowder infantry), but they weren't related to them in any other capacity and weren't parts of the Ottoman forces. There is no evidence that supports any number of Ottoman soldiers in Devlet Giray's army.

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It was a risky gamble: if the Tatars successfully bypass or breach some part of perimeter, then dispersed garrisons most likely won't be able to link up in time to stop them, and northern territories will be completely defenceless in the face of invasion. Ivan stressed to his generals multiple times how important it was for them to constantly keep in check with each other and send scouts to nearby areas, taking notes of any possible enemy activities there. Prince Vorotynsky, Russian commander-in-chief, had to give up the initiative to the enemy and rely on his commanders making right decisions in the right time in order for his defensive strategy to succeed. In turn, if the everything goes according to plan, it will be far easier to pinpoint direct route of enemy movement, and defenders' advantage and combined arms of Russian forces will most likely prove to be overwhelming.

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Tatar forces were spotted by Russian scouts on the banks of Kolomak river in the first days of July. Around 9-11 July entire defensive battleline was put on high alert. Commanders farthest away from discovered actual location of the Khanate's horde left token garrisons behind and set out to meet with the main host. By the 25th of July, when enemy vanguard was sighted near Tula, it became clear that Tatars intended to take the shortest (and most obvious) way north via the Serpukhov road, exactly as Vorotynsky hoped. He quickly concentrated his forces near Serpukhov, and was now standing right in the way of the main bulk of Devlet Giray's army.

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Hasty attempts of Tatar vanguard to cross Oka 20 km south of Serpukhov on the 27th of July were easily repelled by reinforced garrisons. Devlet Giray found himself in a tricky situation: suddenly Tatars weren't able to easily choose the most vulnerable part of the enemy line and had to bruteforce their way through, losing both time and men. Hesitant to throw his army into direct assault, Crimean khan decided to split his troops in three parts, leaving his artillery at Serpukhov and sending one of his flanking divisions to put pressure on Russian garrisons and prevent them from joining up with Vorotynsky. Main army under his direct command turned east, away from the strongest Russian positions, and successfully passed through the safe gap secured earlier by another flanking division.

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Vorotynsky, seeing that there was no longer any reason to hold the line at Oka, rallied his forces and turned north, outrunning khan's army and blocking the way to Moscow at Molodi. Russians organized strong field defences there, including mobile wooden fort - gulyay-gorod - and a series of moats which prevented Tatar cavalry from flanking maneuvers. Vorotynsky also sent forward his vanguard which surprise attacked one of Tatar regiments and threw it back. After Crimean khan sent forth reinforcements, Russians turned their back and lured the enemy towards Molodi. Devlet Giray effectively maneuvered himself into a corner: he has already commited large parts of his army to the battle and it was too late to turn back in orderly fashion, he had no artillery to break enemy defences, and it was impossible to outflank Russians since they were already on his tail.

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Finally answering the first question:

According to the Wikipedia article forthe Battle of Molodi: "[...] close-in fighting made the Tatars' famedskill in archery quite useless [...] Artillery and arquebuses were alsoused by the Russians to great effect." If true, what made one set ofranged weapons effective at closer ranges?

Tatar horsemen had to attack entrenched Russian positions on extremely unfavourable conditions. They couldn't utilize their archery skills to their full potential because enemy positions were heavily fortified and supported by both artillery and horsemen. Crimean army left all of their gunpowder weaponry behind, and they were also very short on time: khan was cut off from his reinforcements and was weary of other Russian detachments showing up later and encircling him from multiple directions. There was no reason to skirmish around enemy camp, and it was impossible to leave them behind, thus all the advantages of light mounted archers were completely nullified. The only possible way to victory, from Tatar perspective, was to try and brute force their way through the Russian defences, which was only possible in direct assault and hand-to-hand combat. All the attempts to break through Vorotynsky's defences failed, and Tatars had to turn back, suffering complete defeat.

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TL; DR: It was not about archery being useless against the muskets, but more so about Tatars finding themselves in unfavourable conditions and being forced to commit to the close combat. This led to them being constantly bombarded by the Russians, who deployed field fortifications to cover themselves from enemy fire and could repel enemy attacks with both infantry fire and artillery.

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Hope it clears things a bit.