(2) holds true for the adjective 真："哪张照片是真的?" = Which photo is the real one?" However (1) does not hold true for 真，because we would say "我真的在听你” rather than "我真地在听你".
What's going on? Is 真的 as a noun-phrase used so frequently that it has been frozen in this form? Are there other examples of the same thing happening with other adjectives?
Here, 真的 is being used as a word (an adverb). When 真的 is used as an adverb, the 的 in 真的 is not interpreted as the particle 的, it's a character in the word 真的, such as in this answer (another example is 似的).
We generally don't add a 地 after an adverb; it would be redundant (it's inherently an adverb, so we don't need to indicate it again via 地). So this is not only the case for 真的, but also the case for many other adverbs like 已经 = "already", 有所 = "somewhat", 经常 = "frequently", 终于 = "finally", etc. If we look the word up in a Chinese-Chinese dictionary, these words are categorized as 「副」 or 副词 (adverb). So we wouldn't write 真的地.
In the special case of 真的, 真 also happens to be a word; it can function as an adverb (my dictionary gives the definition 「副」 确实；实在) in addition to other parts of speech, so if we're using 真 as an adverb, we'd ordinarily omit the 地, i.e., we wouldn't write 真地 either.
We ordinarily add 地 to highlight that we're using a non-adverb (typically an adjective, but also verbs and even whole phrases) as an adverb:
地 (de) is used to turn adjectives into adverbs, and can be thought of as equivalent to the suffix -ly in English.
Chinese Grammar Wiki
For example:
他紧张地站着。 (紧张 is an adjective, but we're using it as an adverb => add a 地.)
他半信半疑地点点头。 (半信半疑 is a set phrase, and since we're using it as an adverb => add a 地.)
There are cases where a 地 can be either added or omitted, such as 反复 = "repeatedly":
他反复地说……。
我反复提醒过他。
I think this is because 反复 has multiple definitions, one of which is an adverb (so it's okay to omit the 地), but we might add a 地 to disambiguate. (Also, I think it's affected by rhythm---whether or not the sentence sounds better with/without the 地.)
Simple rules for 的 and 地:
的 proceeds and modifies a noun or pronoun, such as "真的東西 - a real thing". Note that 真的 acts as an adjective.
地 proceeds and modifies a verb, such as "快快地跑 - speedily run".快快地 acts as an adverb.
