We have a signal $s(t)$.
- If we do an upsampling, does the signal duration increase?
- What is the point of upsampling if the signal time increases?
- Can we do an upsampling if we don't use a shaping filter?
No, if you upsample a signal, its duration (i.e. measured in real-world units like "seconds") does not change.
If your signal $s[n]$ is sampled at a rate $f_s$ Hz, and it is $N$ samples long, then the total duration of the signal is $\frac{N}{f_s}$ seconds.
Say you upsample the signal by a factor $M$, yielding a new signal $s_u[n]$. It will be $MN$ samples long, but it will be sampled at a new rate $Mf_s$. Its duration is therefore $\frac{MN}{Mf_s} = \frac{N}{f_s}$. You can see that the signal duration is the same as $s[n]$.
It's not clear what you mean by a "shaping filter" in your third question.