Expression for asking a question in a way that assumes a certain solution?

A leading question is one that suggests an answer, usually one that the asker assumes or desires.

While it usually is used to mean the question leads into an answer that the asker desire for legal reasons, it certainly works to mean what you are saying - a question that presumes an answer will lead from what they have asked.

Note that the first example you gave wasn't truly a 'leading question', since the asker is setting a specific set of parameters: How to get a cheap taxi to the airport. They have a set goal in mind, but those goals are clear and part of the answer that should be provided. Whereas 'putting a garden shed together with glue' is an assumption by the asker, and thus is a leading question.

Those types of questions are asked with "presupposition"

From MW-Online:

Noun 1. presupposition - the act of presupposing; a supposition made prior to having knowledge (as for the purpose of argument)

So in your example, the question about how to find the cheapest taxi to the airport includes the presupposition that a taxi is the cheapest form of transportation to the airport.

A 'loaded question' is one which is asked in order to obtain an advantage from the answer. E.g. If I ask 'Where can I get a cheap taxi to the airport', I may cunningly be hoping the person I'm asking will offer to take me there in their car. That is just one kind of 'loaded question'. There are many others.