I believe you are using the Google launcher which has the Voice command operations as well as the Cards which you have mentioned (I can't assure you that this answer will work because the root of the phone may hamper the application working but still you can try as these steps are common for all).
And yes you will lose the cards as you are deleting the data but you will not loose if you clearing cache.Clearing cache memory is no where related to any file getting deleted .
Cache memory is just a temporary storage which is used to speed up the loading of any application.If you clear the cache memory then your app may load slow only the first time later it loads fast.
Coming to the voice search crashing after "OK Google" could be related with your mic problem or just a small software bug.Follow these steps to pin-point the main reason of the issue
First enable the speech output from settings>Voice>Speech output to make sure it is really detecting OK Google and not something else.If it's detecting correctly then your microphone is correct.
Second after enabling the speech output you need to 1)force stop then 2)clear the cache.
Third make sure the area around the mic is clean and is free of any obstruction (the mic could contain small and minute dust particles which need to be cleaned only by trained professionals, covered by some accessory).
After that you shall be able to perform voice search directly without manually touching the microphone.
If you still have the problem then you need to get in touch with the Support team which is there in the play store bottom of the app page.