Will the police normally be able to take this further?
If your family member(s) have been assaulted, or harassed (endured unwanted behavior that has caused them to feel threatened, distressed etc) then this should absolutely be reported to the police, every time. A racial element would be considered an aggravating factor.
In terms of the gossip, unless they are directly inciting violence for example, it's less likely to be a police matter. However if it's leading to criminal behavior from others, the police might 'have a word'.
Is the victim able to take this neighbour to civil court for financial compensation and or a restraining order? It’s tricky because most of the times, this neighbour was not the one carrying out the abuse.
The behavior you're describing from the neighbor is slander - making false statements about the victim to others.
While it's possible to sue for slander, it's not easy. Your relative would first need need to secure witnesses to/recordings of the false statements.
They would then need to evidence that the statements caused them 'serious harm' (reputational, financial etc). Being upsetting/offensive isn't enough, the 'harm' must be measurable and the burden of proof would be on your relative.
The whole process is extremely, often prohibitively, expensive.
What they could do (and this is the first stage of civil action anyway) is pay a solicitor to send a Letter Before Action - essentially a warning that they will sue unless the behavior stops.
Restraining orders similarly require evidence of the behavior your relative is asking the court to prohibit.
The family is thinking about renting the property out rather than selling and moving away due to obviously needing to declare this in any sales. They are luckily able to do this. Is this correct?
Landlords aren't legally required to disclose problematic neighbors to tenants.