Is It Allowed to Pray Where a Dog Has Been?
Question

I am in America and there are no mosques nearly to which I can walk or from which I can hear the Adhan.
I have two questions:
The first question is:
Should I give the Adhan for each prayer, knowing that I am going to pray on my own, because there is no musalla (prayer room) in the building and there are few worshippers who pray regularly among the Arabs here, because they are at work during the times of prayer, and the neighbours on my right and left are American.
I am anxious about my situation and I started to offer my prayer in the lobby of the building, and some of the worshippers who have travelled and left me on my own told me that dogs and their owners pass through that place, and it is not permissible to pray in it.
My second question is:
Should I pray there when the dogs come and go in that place, but it is the only place that we think is suitable for praying in congregation?
Praise be to Allah.Do You Have to Say Adhan When Praying Alone?
It is not obligatory to give the Adhan for one who is praying alone;  rather it is Sunnah in his case, and there is a great reward for it.
However, if you raise your voice when giving the Adhan, that is better, but if you give the Adhan in a low voice, there is nothing wrong with that.
Can You Pray Where a Dog Has Been?
With regard to the place being frequented by dogs, this does not mean that it is not allowed to pray there, because the mere fact of a dog passing through a place does not render it impure.
How Dogs Were Handled in Prophet’s Mosque
Al-Bukhari (168) narrated that Ibn `Umar (may Allah be pleased with him) said: I used to stay overnight in the mosque at the time of the Messenger of Allah (blessings and peace of Allah be upon him) when I was young and single, and dogs used to urinate and come and go in the mosque, and they did not sprinkle water over any of that.
The Hadith indicates that the fact that a dog passes through the mosque does not mean that one is not allowed to pray there, and the mosque does not become impure.
With regard to dogs urinating in the mosque, some of the scholars responded that they did not actually urinate inside the mosque, rather they would come and go in the mosque and urinate outside.
Others stated that this occurred before the ruling came that dogs are impure and it is necessary to purify (things and places) of their impurity.
Al-Hafidh Ibn Hajar (may Allah have mercy on him) said:
The most correct opinion is that this happened at the beginning, on the basis of the principle that all things are permissible (unless there is evidence to the contrary), then the command came to honour and purify the mosques, and doors were put on them. (End quote from Fat-h Al-Bari, 1/279)
Shaykh Muhammad ibn Muhammad Al-Mukhtar Ash-Shanqiti (may Allah have mercy on him) said:
There are two issues in this Hadith. The first issue is the coming and going of dogs. The scholars answered that by saying: In the version of this Hadith that mentions (the dogs) coming and going, it refers to them coming and going in the mosque.
With regard to their urinating, that was not in the mosque; rather the coming and going was inside the mosque, but urinating did not happen inside the mosque. Al-Hafidh ibn Hajar (may Allah have mercy on him) referred to this in his commentary on Sahih Al-Bukhari, i.e., Al-Fat-h.
But if we assume that what is meant is that coming and going and urinating all happened in the mosque, then we may say that with regard to urinating inside the mosque, one of the following two scenarios must apply:

Either the dogs urinated and the people were aware of where it happened, in which case there is no confusion concerning it, and this strengthens the view that dogs are not impure, if it is proven that the Prophet (blessings and peace of Allah be upon him) and the Companions knew where it was and prayed in the place where the dogs had urinated. But there is nothing in this Hadith to indicate that.
Or it may be said in response that this happened before the Prophet (blessings and peace of Allah be upon him) instructed people to wash a vessel if a dog licks it. This is the strongest answer. To explain further, the mosque of the Prophet (blessings and peace of Allah be upon him) did not have doors (at that time). There is also a report from Ibn `Umar (may Allah be pleased with him), to which  Al-Hafidh (may Allah have mercy on him) also referred in Al-Fat-h, which states that he paid attention to the mosque after that, and took measures to prevent dogs entering it. This proves that the later development was the Prophet’s paying attention to the mosque. We may also note that the Hadiths that enjoin washing vessels if licked by a dog, were narrated by Abu Hurayrah and `Abdullah ibn Maghfal (may Allah be pleased with them, who both became Muslim later on). Based on that, the scholars said that what is narrated in the Hadith (about dogs coming and going in the mosque) occurred earlier on, and the instructions to wash vessels if licked by a dog is what came later.

The basic principle is that we should follow the later report, which abrogates the previous report. Then there will be no confusion about the matter, which is the coming and going of dogs in the mosque. (End quote from Sharh Sunan At-Tirmidhi)
To learn more, review these responses:
What Happens If a Dog Licks You in Islam
How purification from the Impurity of a dog is done
Is Touching a Dog prohibited?
Does Touching a Dog Break Wudu?
And Allah knows best.