The UK is not in Schengen now, and it would be perverse to try and join, or become associate members of, Schengen after Brexiting. Being in the EFTA would mean

The UK is not in Schengen now, and it would be perverse to try and join, or become associate members of, Schengen after Brexiting. Being in the EFTA would mean continuing to obey EU legislation, continued freedom of movement and paying money into the pot, ie. everything the Brexit campaign was against. So, no, those agreements will likely not remain in place. The EU wil not agree to give the UK all the benefits of EU membership without the costs. There may be other benefits to Brexit, but it will not be the case that Brexit will be good because the UK will negotiate a deal that, of itself, is better than the current deal the UK gets.