eslHQ - hide vs conceal

It's not a matter of collocation but of grammar, meaning and style:

1. Grammar : hide can be transitive or intransitive, while conceal is always transitive. So, for instance, only hide is possible in The children ran away and hid, but both are OK in He was unable to hide/conceal his disgust. A preposition like "underneath" or "among" is outside this distinction - it's just tagged on to the phrase, so could be used with either : The children ran away and hid underneath the stairs/among the trees; They had concealed the guns underneath/among a pile of logs.

2. Meaning : Both hide and conceal mean "put out of sight", but there's a difference : If you "hide" something, it may be that the other person knows perfectly well that it's there, but just temporarily can't see it : ie John and Mary hid and Helen counted to 100 before going to look for them; She hid her face in her hands. However, conceal always has the added meaning that the thing couldn't be seen at all - either because the other person didn't know about it or because it was permanently hidden : The guns were concealed underneath a pile of logs; His face was concealed by a balaclava. (Hide can have this meaning too, and therefore can again be used more widely)

3. Style : conceal is slightly more formal than hide -which is neutral in style. However, this distinction is only slight.

Some concordancer examples which show all of this happening :

If he suffered under cross-examination he hid it well.
... handed over five dates. Eberly devoured one and hid the rest in his sock.
there was a government conspiracy to hide the truth about ....
He hid in his potting shed in Malton ...
The thing, perhaps, would be hidden behind something else.
Police said the bomb was hidden in a pipe
By now Hobart was hidden beneath clouds ...

... and, if he were concealing something,
... a self-portrait in which an outsized apple conceals the painter's features
...and Raisa Gorbachev, once barely able to conceal their mutual dislike
... it was concealed by the snow
... a lamp in which a wide-angle TV camera was concealed.
...you could see the contours, which were concealed by a mantle of dense vegetation.
A pull-out larder is cunningly concealed within cabinets.
...most of our inset gas fires have controls concealed behind the front fender.

So, to answer your question : all of your words would be fine with either verb - as long as the differences in grammar, meaning and style are taken into account.