I have listen that, there are some specific god's and temples where women are not allowed to go and touch the idols. And men only can worship them, or go to their temple or touch them like Shani Dev or Sabrimala also Hanuman ji but I don't know reason for Hanuman ji.
Similarly, Are there any gods and temples only for women, where only women are allowed to enter and priest & god are also women.
Are there any god who listen to the problems of women only?
There are certainly a lot of women-only temples. Two of the famous ones, which I can recall are:
The Kamrupa Temple is a Shakti Peeth, where the yoni of Sati fell. During the menstrual cycle of the presiding deity, Kamakhya, only the female priests are present, and only women are allowed to visit the temple.
During the famous 10 day Attukal Pongala festival, women gather and prepare Pongal. During this time, men are forbidden from visiting the temple. Some 1.5 million women visited it, which became a world record.
Aside: The Chakkulathukavu Temple at Kottayam, celebrates an annual festival of Nari Pooja, during which men are not allowed. However the male priests remain, and they wash the feet of the women.
Example1:
Sadhguru Jaggi Vasudev, from the yogic tradition, he espouses worshipping "Linga bhairavi" , whose temple is at Velliangiri Foothills, Tamilnadu. Men can not enter its inner sanctum.
ref1: Linga Bhairavi is the most exuberant expression of the Divine Feminine, residing in a triangular-shaped abode at the Velliangiri Foothills. http://lingabhairavi.org/about-bhairavi/linga-bhairavi/
ref2: He is quick to follow it up with an analogy of the Linga Bhairavi worship of which he is a known propagator since 2010, wherein men are not allowed to enter the inner sanctum. https://www.thenewsminute.com/article/sadhguru-terms-barring-women-temples-%E2%80%98discretion%E2%80%99-rather-discrimination-38553
Example2:
Ma Panchubarahi temple in Satabhaya village near Kendrapda town in Odisha state of India : Men can’t touch the five idols in this sea beach shrine, men are not allowed into the sanctum sanctorum; only married Dalit women from the local fishing community have the exclusive privilege of performing rituals. There has been no exception for 400 years.
But, the sea has been advancing towards Satabhaya for a while. It has swallowed many houses and agricultural plots. Fifty years ago, the temple was 5km from the beach. Now, only a few metres remain between it and the sea. With rising sea waters — brought on by climate change — threatening the very existence of the temple, the curb has been reluctantly lifted , only for a single day. Compelled to relocate to a new temple 12km inland, the priestesses are left with no option but to allow men into the sanctum sanctorum to transport the heavy black stone idols. “It is not possible for women to pull it off. We need many men and sculptors to move the idols,” Sabita Dalei, one of the five priestesses who work in shifts, says. The rare exercise will take place on Friday (today). Once the 1.5-tonne deities riding piggyback on the male labourers reach their destination in Bagapatia, the priestess will ‘purify’ them with a ritual.
There is a temple in Tamil Nadu, India named Avvayar Amman Temple where women only allowed to worship. But I believe there is a specific duration at that time all people allowed and remaining days, women only allowed.
