2 - Captain mode in the server browser would be lovely. I like the way they did in Star Wars Battlefront 2 in the later versions personally, they had like 10 game modes or something silly but what they did is hid the most popular ones away a little (Galactic Conquest) which encouraged people to play the less popular ones, really good idea.
To the contrary there was an absolutely fantastic game mode in the old game Red Orchestra 2 called Countdown mode, it was a really brilliant mode but they hid it away in a menu for some unknown reason, and literally had a warning saying something along the lines of this mode is difficult only play it if you're good etc, so of course no one played it except for clan matches.
I always think it's a good design decision to make it easy to get in to play the game, but easier still to get into the bits which are less popular but which you are wanting to popularise. A lot of the time the less popular modes are simply not popular because they've been hidden behind a menu. Having people play a diversity of modes also helps keep the game alive for longer, which was always nice.
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3 - Duel is super popular in Mordhau, 5v5 is super popular in CS:GO/DOTA 2, some people enjoy 3v3's. Basically I think as a dev you need to have a map you've spent ages making and have it used in several different ways (e.g. use the same map for Battle, Deathmatch, Duel, 3v3 etc), just change the spawn points, victory points, etc.