I had the same probem a while ago, before starting using Symfony framework.
Just use a function __() which has arameters pageId (or objectId, objectTable described in #2), target language and an optional parameter of fallback (default) language. The default language could be set in some global config in order to have an easier way to change it later.
For storing the content in database i used following structure: (pageId, language, content, variables).
pageId would be a FK to your page you want to translate. if you have other objects, like news, galleries or whatever, just split it into 2 fields objectId, objectTable.
language - obviously it would store the ISO language string EN_en, LT_lt, EN_us etc.
content - the text you want to translate together with the wildcards for variable replacing. Example "Hello mr. %%name%%. Your account balance is %%balance%%."
variables - the json encoded variables. PHP provides functions to quickly parse these. Example "name: Laurynas, balance: 15.23".
you mentioned also slug field. you could freely add it to this table just to have a quick way to search for it.
Your database calls must be reduced to minimum with caching the translations. It must be stored in PHP array, because it is the fastest structure in PHP language. How you will make this caching is up to you. From my experience you should have a folder for each language supported and an array for each pageId. The cache should be rebuilt after you update the translation. ONLY the changed array should be regenerated.
i think i answered that in #2
your idea is perfectly logical. this one is pretty simple and i think will not make you any problems.
URLs should be translated using the stored slugs in the translation table.
Final words
it is always good to research the best practices, but do not reinvent the wheel. just take and use the components from well known frameworks and use them.
take a look at Symfony translation component. It could be a good code base for you.