This forum is dedicated to developer questions related to using Refinitiv APIs.
The best resource for content search and explanation questions is Refinitiv Helpdesk, which you can reach using Contact Us capability in your Eikon application. The moderators on this forum do not have deep expertise in every type of content available through Refinitiv products. Such expertise is available through Refinitiv Helpdesk.
There's no straight answer to your questions. There are numerous definitions for a close price across various markets. Which field you want to use depends on the instrument (or on the asset class and the market). Same goes for when the price is updated. If you need the history for US stocks you can use TR.CLOSEPRICE or TR.PriceClose (see the answer on this thread for discussion on the difference between the two). If you only need the most recent close price and you'd like to have it updated as soon as the exchange publishes the close price after the market close use HST_CLOSE field. For discussion on how stock price history is adjusted for capital change events see the answer on this thread.

If you'd like to find out which field you need to use to get the close price for a specific asset class and market or if you have any further questions about content available through Eikon, please contact Refinitiv Helpdesk.