Учёт расходов помогает мне сэкономить деньги.

Because учёт (meaning keeping track / accounting) typically governs the genitive: учёт чего? → учёт расходов = tracking of expenses.
Расход is a countable “expense,” and in real life you usually mean multiple expenses, so genitive plural расходов is natural.

Мне is the dative case. The verb помогать takes the dative for the person being helped:
помогать кому? → мне, тебе, ему/ей, etc.
So помогает мне = helps me.

A very common pattern is: помогать + dative + infinitive
It means help someone (to) do something:
Учёт расходов помогает мне сэкономить деньги = Tracking expenses helps me save money.

Yes, both are possible, but they differ in meaning:

• сэкономить (perfective) focuses on a result: to save (some amount), to end up saving.
• экономить (imperfective) focuses on the ongoing process/habit: to be saving, to save regularly.

So:

• ...помогает мне сэкономить деньги = helps me manage to save / save up money.
• ...помогает мне экономить деньги = helps me save (as a habit) money.

In Russian, деньги is a plural-only noun (there’s no singular деньга in normal modern usage for “money”).
Here it’s the direct object of сэкономить, so it’s in the accusative plural. For деньги, accusative plural looks the same as nominative plural: деньги.

Yes. Russian word order is flexible and changes emphasis:

• Учёт расходов помогает мне сэкономить деньги. Neutral: the topic is учёт расходов.
• Мне помогает учёт расходов сэкономить деньги. Emphasizes me (as opposed to someone else).
• Сэкономить деньги мне помогает учёт расходов. Emphasizes the result (saving money).

The core grammar (cases/roles) stays the same.

Учёт is broader than “accounting.” It often means keeping records / tracking / monitoring.
So учёт расходов is most naturally expense tracking or keeping track of expenses, not formal бухгалтерия (professional accounting).

Correct spelling is учёт (with ё), and it’s stressed: учёт.
In many texts, ё is often replaced by е (so you may see учет), but it’s the same word. Learners benefit from keeping ё because it signals both pronunciation and stress.

Typical stress:

• учёт (stress on ё)
• расхóдов (stress on о)
• помогáет (stress on а)
• сэкономи́ть (stress on the last и)
• дéньги (stress on е)