All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, you have to know that this religion is sent down by Allaah, the Most-Wise, the All-Knower. He is the One Who knows what is beneficial for His Slaves in this world and in the Hereafter. The Words of Allaah are the Truth and All that Allaah has Legislated is just. Allaah Says (which means): {And the Word of your Lord has been fulfilled in truth and in justice.}[Quran 6:115], i.e. true in information and just in rulings, free from all kinds of lies or injustice. The belief of a Muslim requires that he submits himself to Allaah's Decree. The Muslim's belief that Allaah is Perfect in his Names and Attributes, and that he is the All-Knower, the All-Wise, the All-Aware, and belief in His other Names and Attributes, all this requires from him to firmly believe that Allaah does not legislate except that which is beneficial for His Slaves, and that He does not wrong anyone in His Rulings. It is He Who forbade injustice on Him and made it forbidden among the people. A Muslim may not know the wisdom and the secrets of legislation, so it is not permissible for him to condition his belief on perceiving the wisdom, to an extent that if he knows the wisdom, he believes and if he does not know it, he does not believe. Therefore, you should be careful, and your slogan should be the Saying of Allaah [when speaking about the believers] (which means): {And they say, ''We hear and we obey. [We seek] Your forgiveness, our Lord, and to You is the [final] destination."}[Quran 2:285]. This is just an introductive answer to your misconceptions before we proceed to answer your questions.
As regards your questions, the answer would be as follows:
1) It is not correct to say that the punishment for the woman in most cases is more severe than that of a man. It is related that the man is cursed and there are severe warnings against him in relation to some of his conducts with his wife. For instance the Prophet said: "Allaah cursed the husband who has sex with his wife in her anus." [Abu Daawood] The Prophet further said: "Whoever has sex with a woman in menstruation, or has sex with his wife in her anus, or had been to see a magician, he had indeed disbelieved in what was revealed upon the Prophet Muhammad the Prophet ." [At-Tirmithi] In another narration the Prophet said: "When a husband has two wives and does not act justly between them, he will come on the Day of Judgment with a side of his body hanging down (as a form of punishment)." [Abu Daawood]
2) It is not possible to be certain that the punishment of a disobedient woman is less than that of a husband who hits his wife without any religious reason. Allaah Says (which means): {…But if they obey you [once more], seek no means against them. Indeed, Allaah is ever Exalted and Grand.}[Quran 4:34]. Imaam Ibn Katheer said in relation to the interpretation of the above verse: 'This is a threat to the husbands if they are unjust to their wives without any valid religious reason, as it is Allaah Who is their [wives] guardian and He will avenge those who are unjust to them.' Even if we assume that the punishment of a disobedient woman or the woman who refuses to share the bed with her husband is more severe than the punishment of a man hitting his wife, the harm that results from a woman who refuses to share the bed with her husband is greater than the harm which results from him hitting her, as the husband may resort to adultery because of his wife refusing him to enjoy her, and other harms could result due to her refusal. Moreover, the Prophet clarified the issue of men hitting their wives that it is not a simple matter as he said: "The men who beat their wives are not the best of you.", so how could it be deduced that this is an easy matter, rather this is a severe threat.
3) It is true that Islam legislated that a husband has the right of not spending on his wife if she is disobedient to him, but it is not correct to say that the wife has no right if the husband does not fulfil her rights, as in such a case Islam has given the right for the woman to take the matter to the court in order to remove the harm off her.
4) It is known that in general women are controlled by their emotion, that is why Islam did not put divorce in her hand and prohibited her to ask for divorce without a sound religious reason so that she will not resort to divorce for trivial reasons. It is for this reason that the stance against her is more firm than in relation to the husband. Finally, it should be noted that Islam legislated divorce as the last solution to clarify that it is disliked to resort to it as a means of solving the problems. The Prophet said: "Divorce is the most hated lawful act to Allaah." [Abu Daawood] Although some scholars considered the chain of narrators of this Prophetic narration as weak, yet its meaning is correct.
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Allaah Knows best.