I’ve been adding some artists.
Who are performed by the same person (Jason Dowd). How is the best way to draw the relationship between the two? Or do I need to introduce a 3rd artist which represents the person?
You can create Jason Dowd and use the perform as relationship for both other 2 artists.
Here’s an example of an artist with different names/projects: https://musicbrainz.org/artist/a2af80a6-b3d9-4727-98cb-9f7146f64bd8/relationships
Thanks for this! Good to see some examples 
I’m new to MusicBrainz and am loving what’s being done here.
Is this the recommended way to represent such relationships?
Furthermore - is it possible to than list all releases by the artist “performs as”?
Welcome to MusicBrainz! 
Here’s the guideline for it:
Performance names and legal names
Generally, use the name the artist mainly performs under as the artist name. Alternative names, including any legal names and name variations, should generally be entered as aliases, and can be used in artist credits and relationship credits when appropriate.
In some cases, a person (or, more rarely, a group) can perform under multiple names that they actually consider different projects, and not just alternative names. In that case, you should add each artist separately. If they’re a person, a separate legal name artist should be added, and linked to all performance names with the is person (“performs as”) relationship. In this case, do not add legal name aliases to the performance names. For groups, just link each group to their members.
There are some examples on the wiki page:
https://wiki.musicbrainz.org/Style/Artist#Performance_names_and_legal_names
For your last question, you mean listing all releases combined ? That’s a good one. I don’t know!
I believe not 
As Lotheric says, we can credit other credited names as aliases/ using the ‘credited as’ fields (so, not creating new artists for every variation), and this displays everything in the same artist profile.
Otherwise MB is currently quite bad at displaying related projects etc currently unfortunately.
Stuff like showing relationships/related projects more prominently is still being worked on, eg:
I also have to admit that I’m always not sure about this. Usually, I add a new artist with the legal name, since I’m adding DJs, I hope it makes sense, because usually they are involved in several projects.
However, is the ‘Artist Type’ Person correct in this case? Because if I add the date when the solo project was started, it seems like the person was ‘born’ at that time. (E.g. here: https://musicbrainz.org/artist/8fa4eaee-0e35-4d8b-a45b-e2d1de835717) Maybe musicbrainz should have an artist type that reflect this? I don’t know maybe something like ‘Project’?
I would remove this birth date and set 2010 as the starting date of the performs as relationship.
Yes, sure, that makes sense.