Learn Finnish: Viime vuodesta pitäen minä olen säästänyt rahaa johdonmukaisesti. - Since last year, I have saved money consistently.

Yes, they are completely interchangeable here. Both viime vuodesta pitäen and viime vuodesta lähtien mean "since last year" and both require the preceding word to be in the elative case (-sta/-stä). Lähtien is generally more common in everyday speech, while pitäen can sound slightly more formal or literary, but their meaning is identical.

Why is vuodesta in the elative case but viime doesn't have an -sta ending?

The word viime (last or past) is an indeclinable adjective. This means it never changes its ending to match the noun it modifies, regardless of what case the noun is in. So, even though the postposition pitäen forces vuosi into the elative case (vuodesta), viime stays exactly the same.

What are the building blocks of the adverb johdonmukaisesti (consistently)?

It comes from the adjective johdonmukainen (logical or consistent), which itself is a compound. It is built from johto (lead, direction, or management) in the genitive case (johdon) plus mukainen (according to). The -sti suffix is then added to the adjective stem (johdonmukaise-) to turn it into an adverb.

Could we use the total object (accusative) for money here, like ?