Googe Analytics consultant here (not Google employee).
1. Google Analytics' primary identity signal is a first-party cookie. this is not shared between domains. There is no technical way to link identity between domains with different cookie values.
1a. Google Analytics has built-in library functions to allow site owners to share first-party cookie values between a whitelisted set of domains. This effectively lets one company with multiple sites share a first-party identifier, but still not let anyone (Google or otherwise) link that identity to identities set on other sites.
1b. BUT. But. BUT. Google is rolling out "Google Signals" for Google Analytics, which will use your Google Account as the identity signal instead for users who are logged in to Chrome. This, obviously, lets your identity be correlated across sites.
(Personally, I suspect that the availability of this feature played a part in Google's decision to let Chrome follow the industry towards blocking third-party cookies. But this is a baseless opinion, one step removed from a conspiracy theory.)
2. Google Analytics can link their identifier (the first-party cookie or Google Signals) to your DoubleClick profile via DoubleClick's third-party cookie. The checkbox that does this is unchecked by default. There are many other features of GA that encourage or require you to check this checkbox.
2a. Google's documentation (including legal contracts!) places limits in the data exchanged between the two profiles. Data exchanged does include demographic and interest information from DoubleClick's profile into GA. This is one of the big reasons why people click the checkbox.
To my knowledge, GA data is not used to inform the DoubleClick profile. GA data can be used to build an "audience" in various Google ad platforms, and direct ads to those people specifically, or to use as the basis for a "look-alike audience."
3. Google is a Processor under GDPR for Google Analytics, and a Controller under GDPR for Google Ads. To a first approximation, this means they make the specific legal claim that they do not use GA data for their own purposes. Linking Analytics and Ads data is... complicated and frankly I still haven't gotten an explanation of its legal status that I fully understand.
In my personal opinion, I don't think Google actually uses Google Analytics data. Most Analytics implementations are tire fires, and they can get all the data from other more reliable sources, like Publisher data or Chrome. Given that they have based on their entire GDPR compliance strategy for Analytics on being a Processor, I don't think the risk/reward is there.
(apologies for lack of copy-editing, the thunder's about to take my internet away)