Using present tense in past tense narration

Is it grammatically correct to use the present tense in fiction that’s narrated in the past tense? Sometimes, as a writer, you add "general statements" into your narrative. Example:

But random chance just didn’t sit right with him. Nothing in the world
is truly random.

The second sentence is just a general statement, it isn’t an event that happens. Will "Nothing in the world was truly random" be the correct version, or maybe both versions are acceptable?

Another example:

Derek thought of a simple plan – he’ll leave the Maglite far away from
the tunnel through which the creature comes. The boy himself will hide
behind stalagmites. Then he’ll slip away behind his opponent’s back
while it inspects the "bait". This course of action should allow him
to avoid any risks whatsoever.

In this case, the narrative describes the plan of action in the present tense even if the rest of it is told in the past tense. Would it be grammatically acceptable?

When it comes to writing fiction in the past simple, I didn’t find any decent guides that would mention how different times should interact in the narrative.