Participe Présent- acts as a verb tensmode or as an adjective, correct?

Officially it is not a tense but a mode.

Example: "Le joueur, surprenant cses adversaires, se cache la balle"

The same way you can write : ”Le joueur cache la balle, surprenant ses adversaires.” it’s equivalent.

->Is it a participe présent?

Yes

•Does it act as a verb tense?

Participe is mode, that you don’t conjugate.’infinitive is an other example of a mode. Participe exist in present time (”surprenant”) and past time (”surpris”).

•Does it act as an adjective?

It acts here as a verbal adjective : it has the value of an adjective, is used for an action. In this case, it i used as a consequence of the conjugated verb.

"Le joueur, en surprenant ses adversaires, se cache la balle" ?

This sentence sounds a bit weird to me. 2 solutions for the use of gérondif :
- 2 silmutaneous actions that are not necessarily linked, with addition of the adverb ”tout” : ” "Le joueur, tout en surprenant ses adversaires grâce à une grimace, cache la balle" The player is doing a clown show while at the same moment he’s hiding the ball. 2 ”unrelated actions”
- the mean, how you do something : ”Le joueur surprend ses adversaires en cachant la balle” : this is how he surprises his opponents, by hidding the ball. This is strictly the same idea in the sentence with participe présent : the surprise is the consequence of hidding the ball.

•Is it due to the cosmetic difference alone, that it is missing "en" (indicating the Gérondif form) before "surprenant"?

It is not cosmetic, it has different meanings. But is not simple!

Je ne sais pas vers qui me tourner!

I searched ”participe présent gérondif fle curieux”. Thi page gives (too) long explanations and a table at the end. Hope it helps.

Let’s see if someone else can lso help by giving examples in english. I’m not advanced enough for that.