No, it protects people while they are undergoing gender reassignment via hormones or surgery. It doesn’t explicitly protect a person who is being discriminated against for their gender identity.
No, it doesn’t allow gender self ID but sex reassignment.
Very problamatic
https://www.legislation.gov.uk/ukpga/2010/15/section/7
7Gender reassignment
(1)A person has the protected characteristic of gender reassignment if the person is proposing to undergo, is undergoing or has undergone a process (or part of a process) for the purpose of reassigning the person's sex by changing physiological or other attributes of sex.
(2)A reference to a transsexual person is a reference to a person who has the protected characteristic of gender reassignment.
(3)In relation to the protected characteristic of gender reassignment—
(a)a reference to a person who has a particular protected characteristic is a reference to a transsexual person;
(b)a reference to persons who share a protected characteristic is a reference to transsexual persons.
The Equality Act does need to be amended because it says you can change your sex. You can’t.