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Is the choice of mixins chosen randomly or chosen according to size, date of transaction, or otherwise?

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Currently, it's chosen randomly. Half the fake outputs are chosen over the whole chain, and half over the last 1.8 days. In both cases, a triangular distribution is used over the possible fake outputs based on their order of appearance on the blockchain. See wallet2::get_outs in src/wallet/wallet2.cpp.

There is a patch on Github to switch to a single set, using a gamma distribution over the possible fake outputs' age, as found to be close to the real usage distribution in a paper from Miller et al. See https://github.com/monero-project/monero/pull/3528

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