To clarify what Shineko said above:
The use of 歩いている人 (walk-pres.progressive + person) = walking person (not 歩く).
But in general, modifying a noun with a pres-prog verb form makes the equivalent of, what would be called in English, a participle (=verb acting as adjective; gerund=verb as noun). But be careful:
食べたレストラン = what? You may at first think "a restaurant that ate" (similar to the pattern 食べた人= "a person that ate"). But in this case, it means the "restaurant where you (or the implied subject of 食べる) ate at" - this is one of the common constructions that is commonly analyzed by linguists today studying relative clauses.
In Shineko's example: 家に帰る時、歩く人間を見ました。 Don't necessarily think of it as "in the middle" of the sentence, because you have both an dependent clause (a noun phrase ending in 時) and an independent clause (歩く・・た。） I think you'll find yourself getting stuck as you get to more complicated structures if you keep trying to convert English structure into Japanese structure, or vice-versa. Rather, try to learn Japanese structure independently, without trying to convert every sentence. It's hard to do, as the temptation is very strong, but in my opinion if you learn how to understand the structure and the meaning of the structure conceptually without having to formulate an English translation, then you're better off (it's much easier when you're more advanced to go from the structural intuition into translation rather than the other way around).
学校に行けません、病気ですから。
Technically, when you end a sentence with から・ので・が・けど etc. it is not a full sentence, but a fragment. "I am sick, so..." with the rest of the sentence implied in the context of the dialogue, or previously known to both interlocutors. Therefore, in Shineko's above example, we actually have one sentence and a fragment: 学校に行きません。病気ですから。。 (lit. I'm not going to go to school. I'm sick so..."). These two constructions can easily be combined into one sentence (as you may have already guessed/known): 病気ですから学校に行きません。
And to clarify again (reading through above), the object of a sentence is NEVER marked with a は・が。 は is what you would consider a topic marker, while が is a subject marker (but please, do not let "subject marker" make you think you identify the grammatical subject with が - it's not always the case (and usually is not)). に is considered by many as a particle marking a "goal", or a place/direction where something ends up (this can be an actual place when used with verbs like 行く or it can be the abstract concept of direction when you say someone to someone, or when you change something into something else). の acts either as a nominalizer or a connective particle between nominals, again not demarcating the grammatical subject or object.
