Is double encryption really a bad idea? Are meet-in-the-middle attacks practical at all?
meet-in-the-middle attacks rely on storing the results in a map


Only the naive version of MitM does.

The impractical memory requirement (size and accesses) of naive MitM can be greatly lowered with a relatively modest increase in other computation costs, and the calculation distributed to independent devices. The reference paper is Paul C. van Oorschot and Michael J. Wiener's Parallel Collision Search with Cryptanalytic Applications (in Journal of Cryptology, 1999). It covers MitM in section 5.3.

That's also discussed in this question.


  Is double-encryption a stupid idea


Largely so, because of MitM with such improvements. In the case of AES, using AES-256 is a much better idea than double AES-128: it foils MitM, and is faster.


  Is it true that ECC can be broken with $\mathcal{O}(\sqrt{n})$ complexity?


Yes, that's the cost of solving the Discrete Logarithm in a general cyclic group of order $n$, including defined using point addition on an Elliptic Curve. The reference method is Pollard's rho. That is seldom identified to MitM (as the question does), but there are similarities. Not coincidentally, parallel Pollard's rho is described in section 5.1 of the above paper.