If Qa5+ 14. Qd2 then Bb4 wins the queen.

Yeah, I think after allowing Nxe3 and now this inaccuracy, black should be solidly better here, with a pleasant game to follow. Either the computer is saying white is lost here (which I'm not sure about) or just a solid advantage. Black's development practically plays itself, each piece has at least one good square to look forward to, several come with tempo on the misplaced white pieces. Structurally black's pawn structure is less exposed than white's, the f4 and c4 pawns only serve to leave white's king in a gaping vacuum. You can already see the fragility of white's position in that there are already tactics for black and none for white. Strategically black has accomplished a lot out of the opening, and you might say that black is already strategically winning as white is going to have to sit and think up a serious plan to not be much worse. White's king is going to have a hard time finding a home while black can easily catch up in development with 13...Bb4+ 14. Kd1 (14. Kf2 Qc7 -/+) and 14...0-0. Just that simple line should suffice to leave black permanently better. I'm not sure whether a computer would say that this is an advantage for black (+/-) or just flat out winning (-+) but my spidey-senses say that with perfect play white should be able to find drawing chances (so -/+), but only should they be able to survive without too much material loss until the endgame.

I think white scrapes his way out of danger here, the computer is right IMO. Getting castled ASAP is of great importance to black in order to exploit the exposed white king, otherwise white can use black's stunted development to pull his pieces together.

Yes - but I wanted to avoid the exchange of queens too.

The problem with Nd2? is white is kind of forced into a losing position: 14. Nd2? Bb4?! 15. a3 O-O, and Black can just keep relentlessly attacking the vulnerable queenside. There is a line I think with Bd7 instead of Bb4 but it's a bit more tricky to figure out the best possible moves there, but has the same idea.

Yes I think black has an edge whatever now, but Nd2 was a better try.

I don't see the position being equal but I do think white is making the most of a losing position.

It may well be my computer underestimates the danger of the white king in the centre.

Although the computer evaluates this as equal, any master would definitely give black an edge. Only a computer can play with a vulnerable king, most human players (including Fabiano Caruana in the last game of the candidates) can't hold it all together. Once again black is the one who is strategically better, white is going to have a wretched time finding a plan to consolidate his position before black exploits his weaknesses and black's development still writes itself. I feel like black is going to have to do something majorly wrong to be worse, whereas white can be lost on the flip of a dime. Even from a basic standpoint black has been extremely successful in the opening, if I were guaranteed this position I'd pick this opening up in a heartbeat.

For sure Bc5 is superior. This seems too slow to fully exploit white's weaknesses, if I were in white's shoes I'd be relieved to see this move from black. I might have even considered Kf7 instead of this, just to get in Bc5 and Rd8 ASAP. I still am convinced that black is better, just maybe less preferable now.

Computers aren't good tools for positional analysis. They are great for pinpointing tactical blunders and missed tactical opportunities, but in terms of accurately pinpointing positional play, they cannot match humans. Which is why I only get the tactical analysis done through them and then have a team I work with to analyze my OTB games to see what positional errors may exist or where I need to improve on my studies.

Yeah, the rule of thumb is that simplification generally prefers the side who is weaker. White would happily reach an endgame here, in fact the pawn structure might even favor white in that situation. Bb4 is perfectly fine, if not superior from a positional standpoint.

Computer probably prefers 0-0-0 because if we were to go to an endgame here, white's pawn majority on the queenside would be much stronger (since they would likely be the first side with a passed pawn), possibly even decisive. With the black king in the way of the trio, and with a rook immediately on d8, black has finished his development and can move on to creating a long-term plan to reach a winning endgame.

I don't think my computer understands how vulnerable the white king is in the centre of the board.

I think Qc7 is just a little stronger here.

Surely Qb6 or c7 is preferable to trading for the same reasons as before. White is essentially lost here IMO after Qb6.