I’m new to Libre Office and I can’t find out how to
For best help and answer, always mention OS name, exact LO version and save format. Most solutions are persistent only if documents are saved .odt.
This is the case for your point 2. When Writer recognises a link, it applies character style Internet Link or Visited Internet Link to it. So, if you want to change the appearance, customise thesz character styles.
If you’re new to LO, I recommend you read at least the Writer Guide to learn how to access character styles.
Regarding your point 1, your question is too generic to be answered accurately. From a general perspective, open the side style pane. By default, it displays paragraph styles but you can select the category with a click on the icon in its toolbar. The style for the current cursor position is highlighted.
But, if you practice direct formatting, displayed information is pointless because it corresponds to some underlying style which is overridden by direct formatting.
Your document can be “decorated” with coloured marks when you tick Spotlight below the style list. There are separate check boxes for paragraph and character styles. Note that the resulting display is a bit cluttered and you need to become accustomed to it.