The web-developer don't want to insert Google Analytics code into the website, because he is sure, that it would affect the speed of the website's loading badly, despite the fact that I have pointed at the possibility of using the asynchronous code. What is the real influence of the GA's code on speed of website's loading and working?
How does using of other analytics instruments (for example, Yandex Metrica) on the same site can influence the accuracy or stability of working of Google Analytics? Whether this factor can lower the speed of loading and working of the website in addition?
There are a lot of factors to why or how Google Analytics code may slow down a website. Is it a shared hosting? Where have you placed the analytics code? Did you put it at the top of the pages? Or at the bottom?
Good practise would be to add the analytics code before the </body> tag along with other externally sourced JS.
If Google Analytics code slows down your website, it is highly likely that using other analytics instruments will have the same effect.
You might want to run the website through a site-speed-checker like the one at Pingdom or Google's own to see whether it's the analytics code, or something else like bad compression (if you're not using gzip compression) or high-res uncompressed images etc that are actually slowing down your website.
It is also probably a good idea to test both with the analytics code and without to see if there is a significant change in load time. And please do it for multiple simultaneous requests and not just a single request. If you can provide this data, it might be helpful in understanding what's going on!
Hope this helps!
EDIT: Removed question about servers bandwidth based on comment from Eike Pierstorff!