Is it accurate to credit Bodhidharma ... with the invention of Kung Fu?

No. See my answer in https://www.reddit.com/r/AskHistorians/comments/cxj8bx/how_much_truth_is_there_in_the_theory_that_asian/

Is it accurate to credit ... the Shaolin Temple, with the invention of Kung Fu?

No. Shaolin's early military fame was due to helping Li Shimin, who would become the first Tang emperor (Taizong). This was achieved by their private army, basically a conventional armed force. More on this in https://www.reddit.com/r/AskHistorians/comments/8nk3p2/why_did_orders_of_monks_and_monasteries_in_china/dzwm0t7/

Shaolin became famous for martial arts in the late Ming Dynasty. In the late 16th century, they had become known as a martial arts centre, specialised in the staff as a weapon. In the early 17th century, they became known for unarmed martial arts. This is long after the development of unarmed martial arts in China - Shaolin was not their source. However, this was the time when unarmed martial arts, and armed martial arts such as swordsmanship, were becoming less relevant on the battlefield (dominated as it was by musket and cannon, and massed spearmen). The civilianisation of unarmed martial arts (and swordsmanship) was well underway. The rising fame of Shaolin staff fighting (not a significant military weapon) and unarmed fighting (also not of military importance) is likely to be at least partly due to this civilianisation.

With Shaolin famous, other styles started to advertise connections - sometimes completely fictitious - to Shaolin. One well known example is the legendary histories of the origins of Wing Chun - different branches offer contradictory legends, both claiming a Shaolin origin. One notable exception were early Qing claims made by the "Daoist" internal martial arts, which claimed founding by legendary Daoist figures - this was taking advantage of anti-Qing sentiment and the identification of Buddhism as foreign (like the Qing) and Daoism as Chinese.

The first linkage of Shaolin to Bodhidharma, and the origin of martial arts in China to Bodhidharma is from a 17th century book, Tendon Change Classic (AKA Sinew Transformation Classic), Yijin Jing 易筋經 in Chinese. The foreword in the book attributing the authorship is probably a later addition, and might be as late as the early 19th century.

What did martial practices look like in China prior to Bodhidharma?

The dominant martial art was archery, followed by other armed martial arts (such as swordsmanship) and horsemanship. Archery we know a lot about, and much less about swordsmanship. We know that there were "sword dances", perhaps much like modern Chinese sword forms. The only unarmed martial art mention in sources is wrestling but it's likely people were punching and kicking each other two (the prominence of wrestling is likely due it being an acceptable sporting/ritual activity). But we have no details of specific techniques.

Did he actually exist?

It isn't certain. The earliest sources are contradictory, claiming he was Persian (perhaps Sogdian) and Indian. Later sources are sufficiently mythologised so as to be highly unreliable. But there's no pressing reason to doubt his existence. Certainly, Buddhist missionaries and monks came to China from the Western Regions (i.e., Central Asia). None of the early sources mention any connection to martial arts (or Shaolin).

Further reading:

On Chinese archery: Stephen Selby, Chinese Archery, Hong Kong University Press, 2000.

Overview of Chinese martial arts: Peter Lorge, Chinese Martial Arts: From Antiquity to the Twenty-First Century, Cambridge University Press, 2012.

On Shaolin and martial arts:

• Meir Shahar, The Shaolin Monastery: History, Religion, and the Chinese Martial Arts, University of Hawai'i Press, 2008.

• Lu Zhouxiang, A History of Shaolin: Buddhism, Kung Fu and Identity, Routledge, 2019.