Learn Hardcore Japanese: zyagaimo wo yawarakaku nita ato, sore wo pan de tutunde tabete mita. - After boiling the potatoes until soft, I tried wrapping them in bread and eating them.

Breakdown of jagaimo o yawarakaku nita ato, sore o pan de tsutsunde tabete mita.

Why are there spaces between the Japanese words here? Is that normal?

Not in normal Japanese writing. Standard Japanese is usually written without spaces:

じゃがいもをやわらかく煮たあと、それをパンで包んで食べてみた。

The spaces here are just for learners, to make the parts easier to see.

Why is it やわらかく and not やわらかい?

Because やわらかい is an -i adjective, and when an -i adjective modifies a verb, it usually changes to -く.

So やわらかく is the adverbial form: softly / until soft / in a soft state.

Why is 煮た in the past tense even though it is in the middle of the sentence?

Because 煮た is part of 煮たあと, which means after cooking/boiling.

In Japanese, the plain past form of a verb can be used before a noun or a grammar word like あと to show that one action is completed before another.

So:

This does not mean the sentence is ending there. It just marks that this action happened first.

What exactly does あと mean here? Is it the same as あとで?