This is the place to post questions and discussions on usage and style. The members of the Wordwizard Clubhouse will also often be able to help you to formulate that difficult letter.
1) Ask someone for a drink.
2) Ask someone out for a drink.
3) I asked her for a drink.
4) I asked her to have a drink with me.
To me when you ask someone for a drink, you ask them to give you a drink.
The way that you would normally interpret this expression (i.e. in line with your last sentence) is correct.
The answer to both your questions is therefore 'no'.