@nbhatt The easiest way to do these qs is, go to the final state and write all the loops in it as union (+) sign and then use * to generate infinite of them just like @Sumit Singh Dhami has done.

Kleene's Theorem states that: every regular language may be recognized by some FA, and every FA, language may be represented using a regular expression.(simply by the use of union, intersection, concatenation, kleen closure ..etc)

infact in Ardens thorem we also used these union, closure but here is restrictions

Conditions-

To use Arden’s Theorem, following conditions must be satisfied-

The transition diagram must not have any ∈ transitions.

There must be only a single initial state.

so for constructing regular expression from finite automata we have to use either State elimination method or Arden’s theorem.