I dont use any store, other than accresent, and the built in one, similar to you.
I use obtainium for everything else. Im not familiar with the error your describing in question one, however if you are going to run multiple stores as well as obtainium (obtainium is not a store it is essentially a tool for automating manual installs/updates.) being clear on which app is being used to install and manage (update) each app will matter, particularly if the store detects installed apps and offers to manage updates for you.
However i have had issues when i first started using Obtanium as prior to that i was manually installing and updating my apps from there particular websites (whether it was github or direct downloads from the app developers websites)
You need to make sure you completely remove an app including deleting caches etc (im unsure if just uninstalling an app clears all the caches or not, i suspect it proberly does however i always made sure i force stopped, disabled, cleared storage, cleared cache, and finally uninstalled, when i removed existing apps, cause it seems more thorough) prior to installing it with obtainium.
Regarding the verification, everything i install i have been able to get the keys to check but i do know with many it isn`t common (for me that would and is a deal breaker, id just find something else or do without.) and while i dont know if there is a trusted repository of keys or not, I personally dont like the idea of adding another 3rd party into the mix requiring ultimate trust. thats i guess the benefit of a store, particularly the play store which cant really be faulted from that perspective.
One option you have, (which i have had to do with one major app i needed, when they decided to stop offering it precompiled through github, and instead move the apk to fdroid with only source on github)
is to build the apk yourself from source if it is available, and i wont lie as a non programmer this was a steep learning curve but i managed to plow through and now have a virtually isolated compilation image, on a physically seperate predominately airgapped machine, which i spin up when my daily version checking script informs me a new version exists..
I cant really comment much on 3, when i decided to come to graphene it was after having already made the decision a year prior to degoogle, and the purchase of the phone and installation of gos was a major improvement from what i had been doing, so by that stage i was already comfortable using web based interfaces for things i couldnt get apk`s for, but yeah prior to that being accustomed, to app this, app that, banks, superannuation, goverment, tax, games etc etc etc it was a big change that required accepting in alot of cases less convienience/functionality, but i will say that now after 6 years, im never in the position where i feel like im missing out on anything or where there is something i would like to or need to do and cant.
Regarding having a fake playstore account on a seperate profile thats entirely up to you and what you are prepared to accept, I just dont accept googles terms and conditions, and for me its that simple but i get that is quite a hardline stance for most people. The main problem i see with doing so is your fake profile is subject to all the standard tracking any profile is, and you are gong to need to keep it for updates etc so over time it will build up the same data on you that any profile would.. of course not linked to prehaps your more commonly used identities but google is everywhere nowdays and in particular over the last year i have watched there ai analytics appearing on many more websites i visit were its not just the old school cookie based analytics, but there new ai analytics which from my understanding makes correlation using fingerprinting pretty standardised across so many domains that remaining vigilent and protecting yourself from that is almost impossible even without a google account. (luckily if you employ grainular script blocking with an extension such as noscripts you can at least have insight into which domains are attempting to load this stuff and choose to actively block it.)