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What was the outcome of this as I didn't see if you accepted or didn't accept the calling.    I would agree with this post about accepting the calling - I would but I would be honest to the stake president and seek his council and let him decide if it's right for you.  I am in a bishopric right now.  I am so not even close to being eligible for this calling but like you get the old - you will be bishop next blah blah blah.  
I remember reading a story of a bishop that lost his testimony while he was bishop.  He kept it to himself, did his calling and worked through it for 2 years until one day it came back and he knew the church was true all while he was still bishop.  It was a trial of his faith but he kept moving forward and gave it some time.  
It's ironic that we find people in the church with amazing testimonies and experiences that struggle being charitable and selfless (this is me), and then on the other hand we have you who is full of charity and love and service with little to no testimony of the gospel.  Keep on going, if any of your family or ward finds out your struggles and try to fix you be patient with them.  I would love to give you some of my testimony but alas I can't,  but keep going brother the Lord knows your good heart you will continue to be blessed as you keep trying your best. 

If it's short term the ward you are in now the bishop can okay it but that's typically just for a few weeks or a few months.  We have had a sister in our ward for about a year where she jumps from apartment to apartment and the bishop thought it would be best she just come to our ward since she is all over the place.  If it's long term then you need the stake presidents permission and both stake presidents usually need to agree on it or at least should.
Other cases where I have seen this justified is if their is an issue with ex-spouses or maybe there are members who don't get along.  I even saw a time when a someone was called as a bishop in another stake who was just barely on the boundaries  (the stake he was in didn't know as it happened when there were some boundary changes) - haha 
You do have the right to go to any ward but your records will be where you live so you can't hold a calling or get a temple recommend from a bishop of a ward where your records do not reside. 
I wouldn't be too concerned jumping wards at a young age.  Things get more serious when you buy a house and a lot of thought and prayer should go into where you move. 

1.) I'm finding it annoying when women are still treated as the 'lesser sex' in today's world and in the church .
In the USA and in the LDS Church worldwide, they're not.
2.) Also on the same note, how come there aren't as many women Sunday school presidents or councillors etc,
Sunday School Peesidencies are the responsibility of the Priesthood in the same manner that Gospel teaching is the responsibility of Fathers in the family.
3.) likewise men on primary presidencies,
The rearing of children are the primary responsibility of women in the same manner that the rearing of children are the primary responsibility of Mothers in the family.
 4.) what about 'non practicing' Temple recommend holding gay men teaching, or being on a primary presidency or auxiliaries ? Or non practicing gay women in auxiliary presidencies ?  Mixed presidencies in non priesthood callings .
Male Presidencies - Elders Quorom, Young Men, Sunday School
Female Presidencies - Relief Society, Young Women, Primary
Gay men are males, Gay women are females in the Church.  They are not barred from callings.
 5.). Also why do sisters still have to 'vail their faces' in a certain part of an ordinance in the Temple I always feel it very discriminating towards women when that happens. 
If you're looking for discrimination, you will find it everywhere including places where it doesn't exist.. I suggest you go through the temple again paying close attention to the symbolisms and what they symbolize.  If you're not sure about a certain symbol, like the veil, you can ask any of the temple workers to explain it to you.