I have three questions related to the theory of modular forms and it was frequently asked to me by my collegues and even my invited teacher in our seminars of the number theory at the faculty of sciences of Monastir (Tunisia) and as I was not expert in this theory, I couldn't answer it:

The first one is: Are there examples of usual functions (functions known by everyone) which are modular forms?

The second one is: Given a modular form $f$ of an even weight $k$ and a level $N\geq 1$ over the congruence subgroup $\Gamma_{0}(N),$ we construct its $r-$th symmetric power $Sym^{r}f.$ Is the form $Sym^{r}f$ also a modular form and if yes what are its weight and level?

The last one is: Are there any applications or connections of the theory of modular forms in other field of mathematics? I will be grateful if you reply to my questions.