1. Not unless Her Majesty commits a filicide.
Line of the Succession to the British Throne is determined by Law; it is not up to one's wishes, even those of the Reigning Monarch.
It would take an Act of the Parliament (of the UK and of all the countries of the Realm) to actually remove someone from from Line of the Succession - and a very, very serious reason would be required for that one.
Prince Charles could only loose his succession rights if:
- He marries a Catholic
- Converts to Catholic religion himself
- Abdicates after becoming a King
- Commits a treason and looses his succession rights by an Act of the Parliament
- Commits a highly serious crime (murder or similar) and is removed from Line of the Succession by an Act of the Parliament
Since all of the options mentioned above are highly unlikely, Prince Charles will become King unless he predeceases the Queen.
2. The day Andrew becomes King would be the day Britain becomes Republic.
Prince Charles may have had his share of controversies and scandals but he's a hard-working man, who has faithfully served our country his whole life. Prince Andrew, on the other hand, didn't get his nicknames (including Randy Andy and Airmiles Andy) for nothing.
I actually shuddered at the thought of having Andrew as a King and Beatrice - as his heir.
3. What makes you think the Queen would ever want or consider disinheriting her first-born son?
Andrew may be Her Majesty's favourite privately, but I think ever she knows that he's not fit to be a King.
Monarchy is about continuity and tradition; it's not a popularity contest!
Mind you, if it were, Charles would have won by a landslide - Andrew isn't exactly very popular, is he?