Do we have to advertise job openings internally?

Maybe you don't legally have to advertise a job internally, but politically, it makes good business sense to.
Even if you've analysed your internal talent and think there is no one with the skills or experience to fill the role, employees value the opportunity to apply. It may seem like a waste of time, but every job application and interview an internal person goes to is an opportunity to give them feedback on their skills and career development. HR teams should take extra care to give genuine and valuable feedback to internal candidates that help them develop and not walk away from an application process feeling like the company has already written them off in favour of an external candidate.

No, you are not required to communicate new job openings internally; however there are a lot of benefits to communicating them. For one, an internal employee may want to apply for the job and may be an excellent fit for that new position (even if you didn't think they would be when first reviewing your internal employees). Also, your internal employees may be able to suggest a highly qualified candidate who may not have applied otherwise.

Genrally no, but in circumstances where redundancies may be implemented then genrally yes unless they have no bearing to the skill sets of the people whose roles have been made redundant.

A failure to do so in circumstances where there are transferable skill sets could leave you exposed to an unfair dimsisal claim for failing to conisder suitable alternatve employment.

The equality act in (ACAS UK , 2010) states that it is unlawful to put someone with a protected characteristics at a disadvantage and must be treated fairly and equally. Not giving a fair and equal opportunity to apply for a position within the company, Is this not discrimination? or discriminatory practice? or a discriminate act? It may not be illegal not to advertise, but by not advertising you could be (by action or inaction) discriminating against any or all of the protected characteristics by putting them at a disadvantage. For those who are not categorized as a protected characteristic, they could claim discrimination based on the fact they were offended by a discriminatory practice. They could also claim bully & harassment as possible promotion or their progression has been blocked. An employer has a duty of care to ensure a safe and stress free working environment, which includes bullying. Not sure if the same in all countries but surely worth a look in the Equality Act.

The equality act in (ACAS UK , 2010) states that it is unlawful to put someone with a protected characteriastic at a disadvantage and must be treated fairly and equally. By not giving a fair and equal opportunity to apply for a position within the company. Is this not discrimination, discriminatory practice or a discriminate act? It may not be illegal not to advertise, but by not advertising you could be (by action or inaction) discriminating against any or all of the protected characteristics by putting them at a disadvantage. For any who are not a protective characteristic could claim discrimination based on the fact they can claim that offense was caused by this discriminatory practice. They could also claim bully & harrassment as promotion or their progression has been blocked. An employer has a duty of care to ensure a safe and stress free working environment, which includes bullying. Not sure if the same in all countries but surely worth a look in the Equality Act.