As stated in the answer by Rakesh Joshi, there are certain Mantras which are spoken by God only but those Mantras are not in Sanskrit. Those Mantras are stated in "apabhAshA".
The Mantras are called ShAvar Mantra and plenty such Mantras can be found in the Shavara Tantram.
One Mantra which is to be used on water (such Mantras are called JolporA Mantra) is given below and is stated by Lord Shiva himself:
apabhAshAm pravakshyAmi mantram strivashikarnam |
dhAranamAtrena shaktishAdhanamuttamam ||
achal ghater nichal pAni |
TAhAte upajila kAler vAghini ||
KAler vAghini volom tore | ... etc
Lord Shiva said -
I am telling the Mantra for Stri Vashikarana ( which is used for controlling any lady) in
apabhAshA. By the practice of this Mantra there is definite increase
in power/vitality of the chanter.
So, here, as you can see, Lord Shiva's words are in Sanskrit but the Mantra he gives is not in Sanskrit but in an "apabhAshA".
Here apabhAshA means a language that is not pure as Sanskrit but any commonly spoken language.
There are many persons on this earth (for e.g. the tribal people) who may not pronounce Sanskrit Mantras properly. But since God is all-merciful he cares about everyone.
So, for the benefit of such less privileged persons (if I may say that) plenty of such Mantras are given by Lord Shiva himself in the ShAvara Tantras.
So, the conclusion is, that although more than 99% of the Mantras are in Sanskrit but there are Mantras that are in other languages too.
As regards prayers, then people usually pray in their native languages. So, a Malayali will pray in Malayalam where as a Punjabi will pray in his own language. There is no restriction, to my knowledge, that one needs to pray in a particular language like Sanskrit or any other.