Learn French: Nous ne distinguons guère les virgules pâles. - We barely distinguish the pale commas.

Yes. Just like ne ... jamais (never) or ne ... plus (no longer), ne ... guère forms a two-part negation where guère takes the place of pas. It surrounds the conjugated verb, giving us ne distinguons guère.

Is ne ... guère common in casual spoken French?

Not really. It is considered quite formal or literary. In everyday speech, a French person would be much more likely to use à peine (barely) and say Nous distinguons à peine les virgules or On distingue à peine les virgules.

Why is there a 'u' in distinguons if the present tense ending is just -ons?

The infinitive is distinguer. The u must be kept to maintain the hard 'g' sound (like in 'go') before the vowel o. If we wrote distingons, it would be pronounced with a soft 'zh' sound (like the 'g' in 'mirage').

What are the placement and agreement rules for pâles here?

Like most adjectives describing color, shape, or other objective physical traits in French, pâles directly follows the noun it modifies (virgules). Because pâle already ends in an 'e' in its base singular form, it doesn't change for feminine nouns; it only takes an 's' to match the plural.