1) This may be your only option on creating a clickable URL--there is no way to insert the clickable URL directly into the tooltip, as far as I know.
2) I'm not sure this is possible in Tableau. Hopefully someone with more experience will chime in.
1) You'll need to pre-process your data to extract the URL as a column (or columns to handle multiple URLs in a tweet), then you can put them on the level of detail and create one or more URL actions. It's not pretty, but it'll work.
2) See this KB article, it talks about bar charts in tooltips but it's the same idea of using text characters to build a block: http://kb.tableausoftware.com/articles/knowledgebase/barsintooltips