Detecting voice in a noisy environment
This is in fact a very well suited problem for machine learning and has been explored in the past as published here. It is often called the cocktail party problem, because of the way our human brains can focus on a very particular voice pattern despite being drowned by countless other voices all around us. 

I can think of two ways by which this problem can be approached the first is to transform the spectrogram to only keep the birds chirping. The second, would be to extract the voice patterns from a sample and then substract the extracted voices from the original sample. This second approach would not remove the noise from the truck.

I would go with the former technique. I would get a few thousands clips of birds chirping. Then introduce some other sounds into it. The mixed sample would be my input $X$ and the target $Y$ would be the clean bird sample. This was you can simulate many instances. However, you will need enough bird chirping data to cover the wide distribution which exists for birds making noise.

Q1

For this to work well, you will need A LOT of data. Yes, you should definitely try to get as many samples from wherever you can. You can then randomly introduce these human voices with the bird clips in order to get the dirty signals, then use these to train your model. 

Q2

You most likely will not achieve 100% accuracy with existing machine learning methods. However, if you get close to 90% that is already a miracle and will truly be great. If you are using spectrograms I would first try convolutional neural network (CNN). These have been shown to produce very good results here. The same paper then proposes an autoencoder to clean up the spectrograms. I think this has a high probability of working, but will introduce smoothing to the spectrogram which may distort the birds chirping. Lastly, I would suggest using a generative adversarial network (GAN).

Q3

I would look into the cocktail party problem. You can also get some insight as to what techniques to use by looking at the extensive work that has been done on spectrograms in MRI spectroscopy (MRSI).

Q4

Like I said above I would suggest going from a $n \times n$ sample containing a mixture of sounds to a clean $n \times n$ sample with only the bird chirping. I think this strategy is the one where you will find the most existing literature and many groups have shown it to work.