You can use either "look forward" or "look downward" in English but the instruction "look forward and downward" is a little confusing because the directions are considered somewhat different from each other.
Another complicating factor is the idiom, "forward and upward" which isn't directly related to physical directions. If you were to say "forward and downward" many people would associate the phrase with the idiom and assume you were invoking some form of wordplay.
The alternative you mention in the comments is much more clear:
Look down in front of you.
This is a relatively common expression and means exactly what you want it to mean. You can also omit "down":
Look in front of you.
Most English speakers will look slightly ahead of themselves and then scan downward looking for the intended object.
"[...] questionable and unsafe places to sleep had plunged him into a constant alertness, one that had only been reinforced when [...]"
Grammatical, but weakly written.
*EDIT - questionable = unsafe. you risk watering down the sense of danger. had plunged - why past perfect? also, hyperbole? Constant alertness - if you are not continuously [in focus], could you be said to be alert? Been reinforced - passive is OK, but why? (and, lose tempo.)
"After what he perceived to be an uncertain amount of time [...]"
Grammatical.
"The noise paused in front of the door"
Grammatically correct, semantically invalid, for the reasons you stated. Prefer "the noise stopped"
can a sound "gain proximity" ? (i.e getting closer).
Prefer "draw nearer" or, simply, "intensified," or the like
"[...] he caught a glimpse of a small group of guards facing the door. Somewhere in his mind, he noted their unusual numbers, though it barely sparked any curiosity in him"
Numbers --> Number, singular: a large (unusually large) number
Prefer switch "it" with "this" to reinforce predicate.
"his thoughts had been slowed down to a halt by the bland nature the days had acquired."
Grammatical, but weakly written.
*EDIT - 1) idiomatic and uninspired. This is no place to make suggestions, but as you have asked, why not: "Time now ran together and his thinking, not at all. Yesterday, today, tomorrow: mere words, no longer concepts, no longer tied to anything, any anchor, of sense and sensing. His Being bled through the fifth dimension listlessly..."
Best Answer
Not really. But I understand what you are trying to express in English.
The late Eva Peron of Argentina fame said it best:
Time is my greatest enemy. Evita Peron brainyquotes
An idiom you may consider:
time and tide tarry for no man or time and tide wait for no man TFD