Мне хочется перекусить чем‑нибудь простым, а потом спокойно вернуться к работе.

Мне хочется is an impersonal construction meaning something like “I feel like / I have the desire.” Grammatically, the “experiencer” is in the dative (мне), and хочется is a 3rd‑person singular impersonal form.
Я хочу is more direct/intentional (“I want / I’m going to”). Мне хочется often sounds softer, more about a craving or mood.

In many contexts, yes: Хочется перекусить… can mean “I feel like having a snack…” with мне understood.
But мне is useful when you want to be explicit or contrast with someone else (e.g., мне хочется, а ему не хочется).

Перекусить is perfective: it focuses on completing the snack as a single event (“have a snack (once), grab a bite and be done”).
The imperfective counterpart is перекусывать (habitual/repeated: “to snack,” “to be snacking”).

Because перекусить commonly takes an instrumental complement for “with/by something” meaning “to snack on something.” The instrumental of что‑нибудь is чем‑нибудь.
So: перекусить чем‑нибудь = “have a snack of something / snack on something.”

‑нибудь suggests “some… or other,” non‑specific and often “any suitable one,” especially in contexts of choice or uncertainty.
что‑то / чем‑то is also “something,” but often feels more concrete (“something (I have in mind / some particular thing)”).

Because it agrees with чем‑нибудь (instrumental). Простым describes the “something” you’ll snack on, so it must match case, number, and gender:
чем‑нибудь (instr.) + простым (instr.).

а потом means “and then / and afterwards,” but а often adds a slight contrast or shift of focus (“first this, then that”), not just a neutral sequence.
и потом is possible, but feels more like simple addition; а потом is very common in “do X, then do Y” planning.

It separates two coordinated parts joined by а:
1) Мне хочется перекусить…
2) а потом спокойно вернуться…
Russian punctuation usually requires a comma before а when it connects two clauses/parts like this.

К governs the dative case. Работа → dative singular работе.
Вернуться к работе is the standard phrase for “return to work” (i.e., resume working).

Вернуться is perfective: “to return (and complete the return),” fitting the idea of “snack, then (successfully) get back to work.”
Возвращаться is imperfective: “to be returning / to return (habitually or in process).” In this one-time plan, perfective вернуться is the natural choice.