Is $y[n] = n x[n]$ an LTI system?

is not an LTI system. It is the output of a causal LTI system.

1. How do I know if my signal is LTI?
2. Which is the following is a LTI system?
3. What makes a system LTI?
4. How do you know if a system is linear time-invariant?

How do I know if my signal is LTI?

A signal x[n] is causal if and only if x[n] = 0 for all n < 0. x[n] is causal if and only if x[n]u[n] = x[n] (think about it). An LTI system is causal if and only if its impulse response h[n] is causal. All real-world systems are causal; otherwise they could see into the future!

Which is the following is a LTI system?

Explanation: A system is said to be linear time invariant (LTI) if the input-output characteristics do not change with time. This expression has a coefficient which is a function of time. ∴ the system is time variant.

What makes a system LTI?

LTI systems are those that are both linear and time-invariant. Linear systems have the property that the output is linearly related to the input. Changing the input in a linear way will change the output in the same linear way.

How do you know if a system is linear time-invariant?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).