Lambda calculus :difficulty in getting hang of induction and conversion
In the definition of substitution $[N_1/ x]N$, we describe how to replace all free occurrences of the variable $x$ by the expression $N_1$ throughout the expression $N$.

The formation rules defining the syntax of $\lambda$-calculus expressions $e$ are

$$ N ::= x \mid \lambda x.P \mid N_1 N_2 $$

where $x$ ranges over a set of variables. One should think of the abstraction $\lambda x.P$ as a function with argument $x$ and body $P$ – or using standard programming terminology, we think of it as a procedure with formal parameter $x$ and body $P$.

In $\lambda x.P$, the variable $x$ is not free within $P$, so a substitution $[N/x](\lambda x.P)$ cannot change anything.

Moreover, writing $\lambda N.P$ does not make sense; the argument/formal parameter must be a variable.

If you are still puzzled, think of an applied lambda-calculus with integer numerals and consider the expression $\lambda x. x +7$ that informally denotes a function that adds $7$ to its argument. Your proposed substitution rule would give us that $[14/x](\lambda x. x+7)  = \lambda 14. x +7$. What would that even mean? (I have no idea.)

By the way, the notion of induction is not esoteric at all. Induction is a central proof technique in mathematics and in computer science, and one cannot understand the lambda calculus without being familiar with it. See https://en.wikipedia.org/wiki/Mathematical_induction for an introduction.