Was the questioner's action of performing tayammum and praying alone at the end of the planned journey correct, given the unavailability of water or transportation to the mosque at the beginning of the planned journey, and the lack of response from those with him to the call to prayer?

Tayammum (definition) is not permissible except when one is unable to obtain water or unable to use it, due to the Almighty’s saying: "And if you find no water, then perform tayammum with clean earth." It is obligatory to seek water in the place, and one should not perform tayammum except after being unable to obtain it. If the mosque is close enough that one can reach it and perform ablution before the time of prayer expires, then it is obligatory to go there, even by walking, unless one fears harm. If you performed tayammum when it was not permissible, your prayer is invalid and must be repeated. However, if you performed tayammum when it was permissible, meaning you could not find water and were unable to obtain it before the time of prayer expired, then your prayer is valid. If you prayed individually while being able to pray in congregation, you have sinned, but your prayer is valid.