[Python] Selenium use of Firefox profile

I try to use Selenium Webdriver and Python on Windows 10 system to make some automation of browser actions. But I have this problem: Selenium-started Firefox window doesn't "see" that I am already logged in and target site sends me to login page. So I assumed that Selenium not really uses the profile, but just a copy of it.

I would like to know:

1. Is my conclusion about actual use of copy of profile true?
2. If 1. is true, is there a way to use really everything from existing profile?
3. If my conclusion is not true, please prove it and point me to the direction where I can find out what information can be used for session, why Selenium could fail to send it and how to force it to do so actually.

Edit:

from selenium import webdriver
fp = webdriver.FirefoxProfile('C:/Users/<user name>/AppData/Roaming/Mozilla/Firefox/Profiles/abc3defghij2.ProfileName')
driver = webdriver.Firefox(fp)
driver.get("https://www.example.com/membersarea")

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