TL;DR: Many of these issues will be solved by the upcoming MB provider and by Improve artist matching and combining · Issue #54 · kellnerd/harmony · GitHub.
Exactly, I won’t bother to try multiple URLs per provider for a single artist (or label), there are already too many of these failed URL lookups for my taste, especially with the growing amount of providers.
The only maintainable solution is to have as many standardized URLs in MB as possible, so I hope that I will be able to release the artist linking feature on the release actions page soon 
URLs with country codes are even more problematic in that regard, as there is no ideal solution for these. Best would be to use the region of the artist in most cases and only use other regions for releases which are not available there.
Yes, the problem is that the artist matching algorithm is way too simple right now, it trips over the artists being in a different order for the different sources 
So the merge algorithm starts with the Beatport artists here, thinks the artist credits from the other sources are not compatible and only uses the Beatport ID to resolve to an MBID.
That part is working as intended currently, there is little value in trying to resolve external artist IDs again on the release actions page when the artist MBIDs should already be available via the MB release.
In my development branch the new MB provider is used to lookup the MB release and merge it with the other data, so every (matching) artist should have an MBID on the release actions page once that is deployed.
You are right, the alternative artist values (in grey) do not show all external links. Identification of alternative values is a generic feature which does not know that the external IDs/URLs of the artists could be combined, it just groups values (here: artist credits) which are considered the same and the displayed value is in fact the first one of a group (here: Spotify artist credit).
That is why the second alternative artist credit value has a hyperlinked Spotify logo on the left of each artist. Deezer’s and Tidal’s artist credit are considered the same (in a text representation), so their icons are also displayed to the right of the whole artist credit.
Admittedly this is suboptimal here, I will see if it is possible to address this without too much overhead.
(In my original solution alternative artist credits did not even display the hyperlinked icons because it felt a bit weird to display the same icon left and right of an artist in many cases. But without them it is sometimes impossible to see why artist credits are different, for example Apple would also have the same artist credit text representation as Spotify/Deezer/Tidal, but it is only one artist entity instead of two separate entities.)
The feature is currently only used for pre-releases, for which the Bandcamp provider already has to do the extra request which contains the track image data anyway. For releases which have already been released, the extra request is skipped as it usually contains no additional data which is relevant.
Some metadata providers already have options on how much data they should return, which they use to decide how many extra requests are necessary. This feature is not exposed so far, but I plan to use it to further optimize lookups and to give the user options to lookup additional data. Bandcamp’s track images would be one such case.
Yeah, I should really address this Beatport oddity. I had hoped someone who actually uses Beatport would come up with a clever solution, but I guess I will simply copy the threshold of four release artists from the userscript for now…
Exactly, I already have code to detect duplicate artists for the “Link with MusicBrainz” feature, I guess it can also be used here.