So there are several third-party apps that help you check the history/profile of a character:
- eve who: https://evewho.com/
That one alone will let you see the things you specifically highlight in your post (ie. employment history and current corporation)
- eve hunt: https://eve-hunt.net/ (responding with a 504 currently)
This will give you an idea of the time they predominantly play, the ships and whether they are cyno capable, logi alts, etc.
- zkillboard: https://zkillboard.com/
Especially the stats page for a character, but also their killboard, which will show where they fly predominantly and whether they solo, small gang, large fleet pvp, etc.
Beyond that, currently you can just ask them for an api key and plug it into:
- eve jacknife: http://ridetheclown.com/eveapi/audit.php
This will give you everything. History, assets, wallet, mails, etc. and at an account (not just character) level if you need
Beyond that, if you have their API key and vcode, you can always just go to the XML api and call for whatever information you want:
However, in the next few months, traditional API keys will be useless as CCP have deprecated the XML API and everyone will shift to the Eve Swagger Interface and then provide access to their information via SSO login with authorization to access info.
I expect that between now and the end of the XML api, new third-party apps will appear that allow you to obtain all the information you need, just by having someone login into an app and include a destination for the information to be sent.