Is the pinyin checked?

Yes. Each story is checked for the reading of words with more than one pronunciation, tone changes such as 一 and 不, and word spacing before it goes online.

Should I read Chinese with or without pinyin?

Both, in turn. Pinyin helps you hear the words; reading without it is how you learn the characters. Changing mode between readings gives you both.

Where can I learn pinyin itself?

The pinyin chart on this site covers the tones, the initials and the finals, each with example words you can listen to.

Chinese reading with pinyin

Every story on RealHSK can show pinyin above each word. Turn it on when a text is new, and off when you want to read the characters on their own.

Smart mode sits in between: it shows pinyin only on the words you probably do not know yet, so your eyes stay on the characters you already can read.

How to use pinyin without depending on it

First reading: pinyin on, to get the sounds right.
Second reading: Smart, so pinyin stays only on the new words.
Third reading: pinyin off. Tap a word whenever you need its sound.

Stories with pinyin

Questions

Is the pinyin checked?: Yes. Each story is checked for the reading of words with more than one pronunciation, tone changes such as 一 and 不, and word spacing before it goes online.
Should I read Chinese with or without pinyin?: Both, in turn. Pinyin helps you hear the words; reading without it is how you learn the characters. Changing mode between readings gives you both.
Where can I learn pinyin itself?: The pinyin chart on this site covers the tones, the initials and the finals, each with example words you can listen to.