Hinduism has been generally regarded by many western scholars to be supporting male dominance because of texts such as Manusmriti. However, such texts have been found in various versions with some versions saying women should be adorned and worshipped while other versions having sexist remarks. Furthermore, Shakta traditions of Hinduism believe that the Brahman has female gender. So what is the view of Hinduism on gender-equality and feminism?
Some signs of Kali Yuga as mentioned in Parashara Smriti's 1st chapter touch upo the issue here:
30 & 31. "Religion has been overthrown by irreligion ; and truth indeed by that which is false ; kings have been overpowered by thieves ; males have been subdued by females ; the worship of fire is dying out ; respect to superiors is ceasing to be seen ; and maidens are becoming mothers : this is what invariably happens in the age of Kali.
In general , in Hinduism, male and female are considered as one whole entity with one being incomplete and incompetent to do any good without the other.
For the divine couple, Shiva- Shakti, its being said that Shiva is simply like a corpse without Shakti.
Shivah shakthya yukto yadi bhavati shaktah prabhavitum Na chedevam devo na khalu kusalah spanditumapi.
Lord Shiva, only becomes able. To do creation in this world. along with Shakthi Without her, Even an inch he cannot move
For the ordinary couple too the same has also been said:
The god Brahma cleft his body in two, of yore, Out of one part sprang the husbands, and out of the other the wives. This is what the S'ruti relates. (13)
A man, so long he does not take a wife, is but (a) half (incomplete) being. A half (thing) can not beget. A whole (thing) only can beget. This is the dictum of the S'ruti. (14)
Vyasa Smriti, Chapter 2.
So, this is in general the view of Hinduism on the issue. They are to work as a whole unit to produce something auspicious.
However, what the verses from Parashara Smriti say can also be empirically verified as we can see those things happening in our society today. So, they are also true.
Hinduism view spans all jeevas, in various stages of their lives. So, there are defined dharmas for men, for women, and for various varnas and asramas. Such dharmas again take into account time and space (kAla and dEza). Dharmas are defined for activities that are transactional in nature as well as those that have far-reaching consequences. The basis of defining all these dharmas is that life and the universe are not limited to the here and the now. There are rules that must be followed if life as a whole must endure , thrive and advance across millennia. In addition, each individual jeeva must attain moksha at the end of it all. This is the ultimate goal of Hinduism. So dharma is defined keeping in mind the goals of moksha plus harmonious living during a particular janma/lifetime.
If certain dharmas at times seem biased in favour of one gender or the other, that is because one is not looking at the larger goals stated above. Having said that, Hinduism holds women superior in many ways some of which are mentioned already in the Question ; men are held superior in some other ways. The takeaway is that, there is a balance of reward and responsibility, a division of labour, a sharing of duty to uphold the laws of the universe, and guidance towards achieving the ultimate goal of moksha.