Let's visit the issues one-by-one:
Sati - For a chaste woman who has lost her husband, if she voluntarily prefers to join her husband in afterlife, she is allowed to do so. The sin of suicide does not apply to her and in fact, doing so brings great rewards to her and her husband in svarga. If not, she is allowed to lead a life of strict celibacy and tapasya on earth.
The problem is 'forced Sati' - when the wife does not want to enter the funeral pyre, but the relatives forced her to do so fearing that she may go astray afterwards and damaging her own as well as both families' dignity/honor. Even today, some wives commit suicide through other means when they're unable to bear the loss of their husband. And even today, some are forced by their relatives.
The problem is not Sati itself but whether it is voluntary or forced.
You can read the reasoning behind the original declaration :
"a life of purity and retirement on the part of the widow is more
especially and preferably inculcated.. the governor-general in council
is deeply impressed with the conviction that the abuses in question
cannot be effectually put an end to without abolishing the practice
Many westerners have little regard for chastity. The brides may not be virgins before marriage, and the husbands don't care, and the widows may remarry, again the new husbands don't care. Any case, the reform was done because British had no way to distinguish between voluntary and forced sati.
There can be no reform in the world to prevent a wife from voluntarily joining her husband after death. That is her own strength of chastity.
Child marriage - Again, the issue of chastity comes up. Kama (desire for lust) enters heart around teenage. If the child acts upon this desire - either mentally, or worse, physically, there is very high danger. If the girl loses her virginity, and the guy abandons her, none else would marry her.
To prevent them from going astray and to account for natural urges, Shastras recommend marrying girls before they reach puberty. The girl's parents have the utmost regard for their daughter's well being - they would find a suitable boy who has is from a different Gotra, has finished Veda studies, from a good family, has good character, strength, has desire in the girl (the boy should come asking for girl, not other way round), and highly important - that Jatakam (horoscope) matches so there won't be any untoward accidents or disharmony. Finally, even though marriage is done early, there won't be any physical relations until she has attained puberty, and usually not until a couple years after.
Sometimes mistakes are made when checking jatakam, or there is prarabdha karma (from previous lives), and the husband loses his life early, and the child is widowed and loses out on an entire lifetime.
The problem is not Child marriage itself, but mistakes in jatakam, choosing of bride/groom, and general unawareness of shastra and unwillingness to follow
Again, Westerners have little regard for chastity (see above). They think cutting off the head is the solution for headaches. Now, we're left with headless corpse - you can see how many incidents of pre-marital relations with teenagers happening now even in India, without the protective fence of marriage.
Women entry to Sabarimala - There are 2 issues here - entry of women into sabarimala, and entry women who are having periods (4 days) into any temple. Both are not allowed, but for different reasons - one is an issue of respecting the deity, and the other is an issue of cleanliness.
Ayyappa at Sabarimala has naishtika brahmacharya vrat (lifelong celibacy), so he won't look at any mature women (age 10 - 50 approx.). The men who visit are supposed to do a 40-day period of penance by maintaining celibacy, not eating meat, drinking alcohol, wearing black clothes, and mala, and doing japa. They do this because they're devoted to the deity. By definition, if you are devoted to someone, then you will try to do what makes them happy, and will try to avoid what causes them pain. It is Ayyappa's desire that nothing disturb his vrat and penance. He is not a human, so he is very strong enough to ward off common desires, but if you are a woman who is devoted to him, you will voluntarily avoid going there out of respect for his vow.
Anyone who is unclean should not enter temple. This is basic rule in shastra. Even they should not enter the puja room in their own house.
Definition of unclean - not taken bath after waking up, not washing feet after nature call, not washed hands/mouth after eating, not bathed after sexual union, bleeding from pores or injury, just consumed alcohol or tobacco etc. The list goes on. Whether you are man or woman, you should not enter temple during these circumstances. Women during periods are unclean. So, by definition, to maintain sanctity of temple, they should not enter it. Most women in India today automatically know, and voluntarily follow this rule. It's only the 'reformists' who have no regard for religion who talk otherwise and stir up anti-equality or feminist fervor.