Here are the ones I've been working on and are somewhat critical to my sites

SimplyWiki - this is the main content creation module on all sites I have and it's ready for 2.0 and PHP8

Formulize - I use this on every site, too. It generates contact forms, order forms, request forms. It started out as a XOOPS module, became part of the ImpressCMS catalog, and then a specialized fork of ImpressCMS. Development continues and there are some things Julian has added to his fork that I'd like to see in ImpressCMS. My priority, however, is to maintain functionality on my sites, especially where there are order forms.

xcGallery - I've posted elsewhere on why I chose this over other gallery modules, and it really comes down to how the images are named after uploading. This was the only module that didn't complete obscure the original name of the image. Recommendations from all major search engines and SEO sources is to have a good name for each photo. There is also a good system for mass uploading images, organizing them into albums and categories.

PHP GEDview - it's a module for displaying, tracking, and managing family tree (genealogy) information, but more accurately it is a way to embed this package on an ImpressCMS site. They continue to develop as a standalone package, and they've had some major structural changes to their code in the version that supports PHP 7+. It might be easier to start with their new version and reload the family tree information.

News - I've tried a couple modules and have both the module from Herve and have tried the IPF version from Simon. The main thing I'm looking for from this is the ability to manage permissions by topic and not have to manage it on every post. I will also consider migrating everything to imBlogging once I get an import figured out and then be able to set and use permissions on imTagging.

Downloads - started with WFDownloads. Tried a migration to Downloads and nothing seemed to import. Discovered missing tables in the database used by Downloads that were added in the core, but the tables were never added. This has been addressed in recent releases. I'll need to try again once my sites have the appropriate tables (need to add before upgrading the version of ImpressCMS to keep everything working).

Links - same thing as Downloads. These two aren't as critical, but do add some to the sites. Managing permissions by groups is essential because of the audiences the sites serve.

Forums - moving to iForum from CBB Forum is a bit of a challenge. The official releases of iForum skip compatibility with ImpressCMS releases. I've posted about this before. The parent repository has had some big changes, looks like in prepration for ImpressCMS TNG and composer.

I've linked to my repositories (except for News - I haven't created a fork for it yet) because I don't know that I've submitted pull requests into the parent repositories to keep them in sync.

Re: Profile - thanks.

Re: ICMS 2.0 - I'm noticing a debug message occasionally about being unable to write session data at the close of a session. It doesn't seem to hinder anything and is not constant. May be related to your blank page after some time has elapsed?

Profile needs lots of fundamental security  fixes, and there is at this moment nobody maintaining it. More details on H1.

What's the latest version of the profile module? I had version 1.3 present and not installed on the SimplyWiki site and when I upgraded it to ICMS 2.0, the module admin page was broken - lots of old class and object references. Once I removed the folder, everything was fine.

BTW - www.simplywiki.org is now running on ImpressCMS 2.0!

well, MariaDB should, in theory, be compatible with MySQL, but there will of course always be subtle differences in how they work. But it's becoming a popular alternative to Oracle's MySQL so it would be logical to verify the compatibility.

I was first thinking of patching up the downloads module, to have a more or less quick fix. But given the number of issues you encountered already, perhaps it will be faster to re-start from scratch then. I've been analysing some parts for several months now, I'll see how it goes.

When it comes to modules that would be nice to get to work on 2.0 : imbuilding could definitely use an update, both in its working (I never got it to work in its latest version) and in the code it generates.