Computer theory/ automata example help
There are online lecture notes which give algorithms for getting rid of $\epsilon$ productions ($\epsilon$ is another name for $\Lambda$) and for converting arbitrary grammars into Chomsky normal form. Both are reasonably simple. There is also an algorithm for converting a context-free grammar to a non-deterministic PDA, but if I remember correctly you first have to convert your grammar to Greibach normal form, so it might be better to understand what the language is and come up with a PDA for it directly.

Since you're taking this course online, I think it will be advantageous for you to find useful lecture notes online yourself, as part of your general education. Finding stuff over the internet is extremely useful, and if that's the only thing you get out of this course, you've already benefitted a lot.

I can illustrate the algorithms by solving some of your examples. In order to eliminate $\epsilon$-productions from your (i), the idea is that for every production that has $X$ in it, we create another one in which $X$ is missing. So we add productions $S \to a | b$. This works in general, but has to be applied iteratively.

In order to convert your (i) to Chomsky normal form, we only need to "rename" $S$: replace $S \to SS$ with $S \to TT$, and add $T \to TT|a$. Other cases require other operations; for example, if you had $A \to BCD$ then you would replace it with $A \to ED$ and $E \to BC$; and if you had $A \to Bc$ then you would replace it with $A \to BC$ and $C \to c$. This should be enough for you to work out the other parts of this question.