There is no way in Selenium to read the request or response headers. You could do it by instructing your browser to connect through a proxy that records this kind of information.
The usual way to change the user agent for Firefox is to set the variable "general.useragent.override" in your Firefox profile. Note that this is independent from Selenium.
You can direct Selenium to use a profile different from the default one, like this:
from selenium import webdriver
profile = webdriver.FirefoxProfile()
profile.set_preference("general.useragent.override", "whatever you want")
driver = webdriver.Firefox(profile)
With Chrome, what you want to do is use the user-agent command line option. Again, this is not a Selenium thing. You can invoke Chrome at the command line with chrome --user-agent=foo to set the agent to the value foo.
With Selenium you set it like this:
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
opts = Options()
opts.add_argument("user-agent=whatever you want")
driver = webdriver.Chrome(chrome_options=opts)
Both methods above were tested and found to work. I don't know about other browsers.
Selenium does not have methods to query the user agent from an instance of WebDriver. Even in the case of Firefox, you cannot discover the default user agent by checking what general.useragent.override would be if not set to a custom value. (This setting does not exist before it is set to some value.)
Once the browser is started, however, you can get the user agent by executing:
agent = driver.execute_script("return navigator.userAgent")
The agent variable will contain the user agent.