I am particularly interested in Document Libraries, but in terms of general SharePoint lists, can anyone answer the following...?
The exact answers have already been given, however I do feel I should add this warning:
This might be one of those situations where if you have to ask, you can't afford it.
So if you find yourself approaching the limits posted earlier, think long and hard about what you are trying to do, and make sure you're not doing it wrong.
Beware, the Performance of SiteDataQuery degrades heavily he more subsites you have. A hundred subsites can take 20 seconds to query.
There is documented guidance for Microsoft® Office SharePoint® Server 2007 regarding the maximum size of lists and list containers. For typical customer scenarios in which the standard Office SharePoint Server 2007 browser-based user interface is used, the recommendation is that a single list should not have more than 2,000 items per list container. A container in this case means the root of the list, as well as any folders in the list — a folder is a container because other list items are stored within it. A folder can contain items from the list as well as other folders, and each subfolder can contain more of each, and so on. For example, that means that you could have a list with 1,990 items in the root of the site, 10 folders that each contain 2,000 items, and so on. The maximum number of items supported in a list with recursive folders is 5 million items.
Link To Resource
SharePoint 2013:
What is the maximum number of items that a SharePoint list can contain? 30.000.000.
What is the maximum number of lists that a single SharePoint server can host? I could not find the answer to this question.
When the number of items in the list approaches the maximum, does filtering slow down, and if so, what can be done to improve it? The maximum of 30.000.000 not a hard boundary, but the limit has been found by testing the product. So a performance penalty is to be expected if this limit is exceeded.
Answers found in Software boundaries and limits for SharePoint 2013.
http://blah.winsmarts.com/2008-4-SharePoint_limits.aspx
for #3: you can index specific columns in a list, but you should still keep the sizes down.