What are the requirements for an entity to be granted such status?
There's no exact criteria or process to be granted observer status. An entity just needs to have "received a standing invitation to participate as observers".
The present document contains the list in alphabetical order of non-Member States, entities and organizations having received a standing invitation to participate as observers in the sessions and the work of the General Assembly.
As quoted from The Telegraph:
The United Nations grants observer status not only to states, but also to international bodies such as the International Criminal Court or regional organisations such as the European Union.
There are no clear procedures on how to become an observer, and associated powers vary accordingly. As a general rule, observer entities have access to most meetings and relevant documentation, but are not allowed to vote.
Observer status can be granted through a UN resolution which was the case for Palestine.
Similarly, there's also no exact process for granting entities permanent observer status as seen from this UN FAQ and it's considered on a case-by-case basis by the General Assembly:
The United Nations General Assembly may grant non-member states, international organizations and other entities Permanent Observer Status.
The UN Charter and the General Assembly Rules of Procedure have no provisions related to granting permanent observer status.
The process is described in a legal opinion of 15 August 2008, published in the 2008 United Nations Juridical Yearbook, p. 438 (in English), part B, paragraphs 8-11.
Permanent Observers may participate in the sessions and workings of the General Assembly and maintain missions at the UN Headquarters.