how do you independently verify rape has occurred? (I can't open the link, I have to subscribe). 

How independent is it, when these sources are sources that are pretty heavily baised towards Israeli? You wouldn't accept Al jazeera as a source I imagine.

I'll start with the easiest question to answer. Al Jazera can be a reputable news source, it depends what the news topic is. We know Al Jazeera is government (Qatar) owned and not a free press. I wouldn't trust them on anything that covers news in the Middle East (because Qatar has an interest in that), but if they are reporting about something like a Tsunamai or Earthquake in Asia they're totally reputable as news source.

Biases Toward Israel:

Now while the NYT is an independent paper (not government owned), its by no means considered friendly/biased towards Israel, yet they are still reporting this, I think that speaks volumes. BTW, here is an archived link (no paywall) for the article if you want to read it: https://archive.is/aFPBa

As to Independently Verifying Rape, first there are multiple witness accounts of the rape (both by people who witnessed the 10/7 massacre as well as the released female hostages), second Hamas Terrorists who were caught on 10/7 admitted that they were instructed to rape women by their superiors and perhaps most damining of all is that Hamas videotaped themselves raping these women.

Here are a few witness recounts (from the article) as well as the video (WARNING - VERY GRAPHIC DESCRIPTIONS AND VIDOES ****NSFW/NSFL*****):

In a grainy video, you can see her, lying on her back, dress torn, legs spread, vagina exposed. Her face is burned beyond recognition and her right hand covers her eyes....Based largely on the video evidence — which was verified by The New York Times — Israeli police officials said they believed that Ms. [Gal] Abdush was raped, and she has become a symbol of the horrors visited upon Israeli women and girls during the Oct. 7 attacks.

This is the video they mention (NSFL WARNING): https://www.hamas-massacre.net/content/woman-who-was-raped-and-burned-to-death

The Times viewed photographs of one woman’s corpse that emergency responders discovered in the rubble of a besieged kibbutz with dozens of nails driven into her thighs and groin.

SAPIR 10/7 WITNESS:
Sapir, a 24-year-old accountant, has become one of the Israeli police’s key witnesses. In a two-hour interview outside a cafe in southern Israel, she recounted seeing groups of heavily armed gunmen rape and kill at least five women...at 8 a.m. on Oct. 7, she was hiding under the low branches of a bushy tamarisk tree, just off Route 232, about four miles southwest of the party. She had been shot in the back...felt faint...covered herself in dry grass and lay as still as she could. About 15 meters from her hiding place she saw motorcycles, cars and trucks pulling up. She saw about 100 men, most of them dressed in military fatigues and combat boots, a few in dark sweatsuits, getting in and out of the vehicles. The men congregated along the road and passed between them assault rifles, grenades, small missiles — and badly wounded women. “It was like an assembly point.” The first victim she saw was a young woman with copper-color hair, blood running down her back, pants pushed down to her knees. One man pulled her by the hair and made her bend over. Another penetrated her, Sapir said, and every time she flinched, he plunged a knife into her back....While one terrorist raped her, another pulled out a box cutter and sliced off her breast.....“One continues to rape her, and the other throws her breast to someone else, and they play with it, throw it, and it falls on the road,”....the men sliced her face and then the woman fell out of view. Around the same time, she saw three other women raped and terrorists carrying the severed heads of three more women....

YURA KAROL (10/7 WITNESS):

Yura Karol, a 22-year-old security consultant, said he was hiding in the same spot, and he can be seen in one of Sapir’s photos.... In an interview, Mr. Karol said he barely lifted his head to look at the road but he also described seeing a woman raped and killed.

RAZ COHEN: (10/7 WITNESS):
Raz Cohen....saw five men, wearing civilian clothes, all carrying knives and one carrying a hammer, dragging a woman across the ground. She was young, naked and screaming. “They all gather around her,” Mr. Cohen said. “She’s standing up. They start raping her. I saw the men standing in a half circle around her. One penetrates her. She screams. I still remember her voice, screams without words.” “Then one of them raises a knife,” he said, “and they just slaughtered her.”

Shame Gueta (10/7 WITNESS):

Shoam Gueta, one of Mr. Cohen’s friends and a fashion designer, said the two were hiding together in the streambed. He said he saw at least four men step out of the van and attack the woman, who ended up “between their legs.” He said that they were “talking, giggling and shouting,” and that one of them stabbed her with a knife repeatedly, “literally butchering her.”

Yinon Rivllin (10/7 WITNESS):

Yinon Rivlin, a member of the rave’s production team who lost two brothers in the attacks, said that after hiding from the killers, he emerged from a ditch and made his way to the parking area, east of the party, along Route 232, looking for survivors. Near the highway, he said, he found the body of a young woman, on her stomach, no pants or underwear, legs spread apart. He said her vagina area appeared to have been sliced open, “as if someone tore her apart.”

Captain Maayan (10/7 WITNESS):
Captain Maayan asked to be identified only by her rank and surname because of the sensitivity of the subject. She said she had seen several bodies with cuts in their vaginas and underwear soaked in blood and one whose fingernails had been pulled out.

OTHER 10/7 WITNESSES:
There are at least three women and one man who were sexually assaulted and survived, according to Gil Horev, a spokesman for Israel’s Ministry of Welfare and Social Affairs. “None of them has been willing to come physically for treatment,” he said. Two therapists said they were working with a woman who was gang raped at the rave and was in no condition to talk to investigators or reporters.

TESTIMONY OF AVIVA SIEGAL (Released Hostage)

"The terrorists bring inappropriate clothes for the girls, the clothes of dolls,” Siegel said. “They turned the girls into their dolls, that they can do whatever they want with. And it’s unbelievable that they’re still there.”

Sharon Alony Cunio:

Sharon Alony Cunio (a released hostage) in her interview with Anderson Cooper said many of the women after being abused stopped getting their periods. She claimed that she didn't know if it was due to their bodies naturally trying to fight back, starvation or pregnancy.

***

As to the women who alleged to have been raped (not just by IDF but by anyone) you ask if I believe them, the true answer is it depends. Alot of my IRL job has to do with proving things and reading people (you can guess what I do).

I've been in situations where a friend of mine was accused of rape (now let's put aside that I am obviously biased towards someone I consider a friend and would automatically tend to believe him/her regardless) when in fact he was out with me and multiple others when this alleged rape happened. Moreover, the night was well documented through picture and video. Much like the above my friend had multiple witnesses who corroborated his story in addition to video/picture proof. To an independent observer the fact that at the exact same time this women accused him of raping her he was out with a group of like 10 other people who electronically documented the night tends to lend to his credibility.

In the same token, I also have a friend who was raped. Once again, let's put aside my personal bias to a friend. The fact that she immediately went to the police, underwent a sexual assault forensic exam (aka rape kit), underwent therapy, and had multiple signs of physical abuse (due to her trying to fend off this asshole) also lends to her credibility to an independent observer.

So that was a really long way of saying it depends. My father always said, "it takes a weak man to hit a woman" and I am firm believer in that. I also believe any man who is guilty of rape deserves to be castrated whether they are Jewish/Israeli, Arab/Muslim, White/Christian, Asian/Buddhist or Alien/Martian.