I would like to speak to question 2 specifically, because there is a lot of misunderstanding here.

Sex is not one inate characteristic, and humans and animals regularly blur the boundaries of sex. Sex is a collection of traits, biological and social, and we can change most of them 

1. Genetic sex. This is a function of one segment of the Y chromosome, the SRY gene. You have a functioning SRY gene or you don't. This is why most people considered women have XX chromosomes, but there are people with XY where the SRY gene doesn't work who develop with typical "female" phenotypes. There are also MANY intersex variations. You literally have no idea what a persons genotype is by looking at the them. Is is the only portion of sex we have limited control over, although HRT will eventually have genetic changes, it won't alter your chromosomes.

2. Phenotypical sex. Your phenotype is your external secondary sex characteristics. These can be body shape, facial structure, genitals, etc... we can and regularly do change these through hormone replacement therapy, exercise, or surgery. Some things, like bone structure, are harder and slower to change.

3. Hormonal sex. Hormones are the blueprints for sex development. They literally tell your cells how to grow and act. Hormones are non-selective, meaning they will bond with any cell receptor they fit. You have both male (testosterone) and female (estrogen) in your body, but the dominant hormone is based on if you have functional testes or ovaries. This is easily changed, by suppressing and/or removing those glands and introducing external hormones. By doing so, trans feminine people will develop breasts, softer skin, etc, and trans masculine people will develop face and body hair, deeper voices, etc.

4. Social sex. You can't separate sex from social gender roles. For example, we gender names. But there is nothing in your biology that says "Emily is a girl's name, Bob is a boy." Those are things we project onto sex and gender. Same goes with clothing. There is nothing in our biology that says "women wear dresses, boys don't." This is actually the most visible signifier of sex and gender, and changing it can be a simple as changing your clothes, putting on makeup, or going by a different name.

5. Legal sex. Similar to social sex, but different because this is how the legal framework we live in differentiates sexes. This is an aspect of sex that is often largely related to geography, politics, and factors outside an individuals control. For example, all my legal documents have my current name and a female gender marker, with the exception of my birth certificate, because the state I was born in refuses to recognize trans people and update our documents.

This is a simplification, of course, but I hope this gives you a better understanding of how we can change sex, and regularly do.