If it is usual occurrence, does it mean that my one gene can change its location from one chromosome to another?
Yes of course; they are not like tandem duplications.
However, some transposons have site preferences; for example the Tn7 transposon.
I don't know what you mean by original location. Some transposons, especially LINEs, have expanded a lot in the human genome. For any individual you can check the germ cells for a reliable estimate on the original positions. There are mechanisms such as piRNA mediated silencing that suppress transposon activity in germ cells. The genome of the germ cells also tells you what exactly will be inherited by the offsprings.
Transposons are specialized sequences of DNA that are part of a larger group termed mobile genetic elements. They can move from one position in the genome to another on the same chromosome or another. A specific enzyme called transposase, usually encoded by the transposon itself, acts on specific DNA sequences at each end of the transposon, causing it to insert into a new target DNA site (Alberts et al, 2015). Not only is this a source of genetic variation, genes carried in this way can convey great advantages such as carrying antibiotic resistance in bacterial cells.