I'm not native Russian so I'm not 100% on that half of the discussion. Grain of salt recommended.

English doesn't distinguish between basically any of the Russian participles, all of the active ones are -ing ending in English. (the others are -ed/-en, bent, shaken, etc.)
I'd like some confirmation on this; I believe past active and present active differ only in what they can refer to. The adverbial participles are made to match with a verb, in the same way adjectives do to nouns, SOOoo, the idea is that a past adverb matches a past conjugated verb, and a present adverb to a present verb. Thus, I propose your sentence should include ожидав and so on.

Perfective and Imperfective probably way over my head, but a small voice in my head whispers увидеть would fit here.

I believe that should be передо мной , not menja, because he is staying in place before him, rather than moving into the space before him [something "standing" doesn't really involve].

In that clause, the one who смотрит is the one whose beloved town it is. It may be that свой doesn't ever refer to participles, and that it always goes all the way back to the main conjugated verb's subject of the sentence: я. IDUNNO, Very good question.

он не был там , this may be correct, we'll wait for a Russian on this one as well, but I think it would sound more Russian as: но его там не было [word order up to you]. Same change with старик in the previous sentence

Comma placement is... Unsure at best for me. I believe the golden rule is ONLY ever place commas to segregate verb-like-things in camps. The idea being, that adverbial participles can have their own objects [things in the accusative case and whatnot] so in order to draw boundaries we place commas, so that when you're mixing up word order you know how much of the words can be linked to which verb-like-thing.

The sentence without any changes but comma placement could be:
...и понял, что старик больше не был в поле зрения. Я обвёл кругом малинкого дома на крыше, в любую минуту ожидая видеть его, стоя передо меня руки за спиной, смотря на свой любимы город;- но он не был там. (the last 5 words are artistically set apart so comma versus semicolon, the difference is up to you)

руки за спиной is in the nominative plural.... This may be a problem. In english we shove word phrases in there indiscriminately, however I think this could cause confusion in Russian on minor levels. Perhaps tie the phrase down to a preposition like: с(o) его/своими руками за спиной, though that still doesn't seem quite perfect =/

смотря and стоя can not be a adverbs here because they are referring to 'его' not обвёл, therefore they would be an active past participle declined in the accusative-animate.

... И понял, что старика больше не было в поле зрения. Я обвёл кругом на крыше маленького дома, ожидая в любую минуту увидеть его, стоявшего передо мной с руками его за спиной, смотревшего на его любимый город; а его там и не было.

The specifics of vocabulary are beyond me though I propose:
дома perhaps здания

обвёл perhaps обходил? Though I think обходить/обойти mean more around a specific obstacle than around an area. I would put my money on imperfective, whichever verb, due to all the detail added to the word being so... Temporally extensive.

и can also be a particle [not participle ], in a fantastically useful way. Wiktionary's explanation:
(preceding a verb) Emphasizes the truth of the following verb. Note that "есть ‎(jestʹ)" is also used, which is usually omitted.
Which is basically saying if быть is the verb emphasized, it is not uncommon to see есть brought back out of omission.
In our case the verb is быть in the past tense, which doesn't get omitted anyway.