I'm not a native speaker, but I've been working in Japanese for decades, and working on Japanese (i.e. studying it) for about a decade longer.
Are both forms [林檎 and 苹果] used by Japanese people?
Let's look at these in turn.
Shogakukan's 国語大辞典【こくごだいじてん】 (KDJ) is a great dictionary for learning about etymologies and term histories, as this dictionary is one of the few to include such details. Kotobank includes KDJ material, but as we saw above for 苹果, Kotobank's entry page doesn't have anything from the KDJ -- because the KDJ has no entry for this term.
However, the KDJ does have an entry for 林檎, as we see here. This kanji spelling has multiple possible readings -- りゅうごう, りんご, and りんき. Due to an unfortunate website redesign several months ago, Kotobank's pages no longer clearly indicate which dictionary definition is for which reading, so sometimes you have to read very carefully. I happen to have a local copy of the KDJ with a less-obfuscated layout. Here are the basic details:
林檎 -- りゅうごう reading
First cited in 934 in the 10-scroll edition of the 和名【わみょう】類聚【るいじゅ】抄【しょう】, a reference work somewhere between a dictionary and an encyclopedia.
The reading りゅう for 林 is explained as an orthographic (spelling) variation for ん, since this nasalized sound had various spellings in ancient times -- the ん kana is relatively recent, and is actually originally a 変体仮名【へんたいがな】 or "variant kana" for む.
林檎 -- りんき reading
First cited in roughly 1181 in the 色葉字類抄【いろはじるいしょう】, another early reference work.
The き reading for 檎 is a non-standard variation of the expected 漢音【かんおん】 of きん. In general, 漢音【かんおん】 readings of kanji are slightly younger than the 呉音【ごおん】 readings, so it makes sense historically that the りんき reading would be younger.
林檎 -- りんご reading
First cited as the oldest variation in 918, in yet another early reference work, the 本草和名【ほんぞうわみょう】.
The sense has changed somewhat over time. Back in 918, the apple that you and I are familiar with -- ''Malus domestica'' -- wasn't available yet in Japan, and thus this term referred instead to what is today called the 和林檎【わりんご】, ''Malus asiatica'', also known in English as the "Chinese pearleaf crabapple". Once ''Malus domestica'' became known in Japan, the term 林檎 was applied to this as well.
Much like Chocolate's comment on the question post, I never encountered 苹果 until I took Chinese in university. This Chinese term has two spellings:
- 蘋果 -- traditional
- 苹果 -- simplified
In the first character in the simplified form, 苹, the main component under the 艹 is a form of 平. In 苹, the two tick marks are slanting outward from the top. The standard Japanese form of 平 has the two tick marks slanting inward from the top. This is one clue that this might not be a very old Japanese term.
Another hint is that various monolingual Japanese dictionaries either don't have any entry for 苹果, or just define it as a synonym for リンゴ. See the relevant page at dictionary aggregator websites Weblio and Kotobank.
At any rate, we can see that this term 林檎 has a long history in Japanese, while the term 苹果 appears to have a much scantier presence in the language.
The superficial similarities in the Japanese reading ringo for 林檎, and the Mandarin Chinese reading píngguǒ for 苹果, are purely coincidental.