Minor Races?

It depends on what you are looking for in the game. Having the minors in a game provides more options for diplomacy (e.g., buying/selling techs, establishing treaties, using them as proxies in a war.), economy (e.g., establishing trade routes with them), and military (e.g., conquering them).

If the major races provide enough options for you, then you can leave the minors out. If you want more, then the minors are good way to achieve that.

That's one of their purposes. However, as I said above, there is a lot more you can do with them, than just get a high-PQ world.

Yes. Once you've conquered 2-3 races (major or minor), your diplomatic relations with the other races will drop, because they see you as a conquerer, and fear, that they are next.

Primarily for the reasons above. However, I'm playing with my mod, Autumn Twilight. In it, I changed the minors to be able to colonise, and I also made them smarter. This means, that the minors are able to form small empires. Sometimes,  they even manage to rival the major races. This provides much more of a challenge, and I find it more fun.

I like randomizing the number of minor races.  They never break a game, but they add lots of opportunity for individual actions that shape the game.  If nothing else, it changes things according to who gets the resources they often claim but can't hold against determined aggressors.

They do get conquered a lot.  Sometimes it just doesn't work out that way and that adds to the variation from game to game.

Then again, the major races often get conquered in my games, so the minor races shouldn't feel so bad about being targets.

Minors can be much less of a pushover if their tech development is accelerated.

Minor races also buy the player "time" as the most aggressive AIs will generally go after them first, instead of the player.

On the higher difficulties especially, minor AIs are revenue sources in the early and early-middle game.  With tech trading allowed, minor AIs are also a source of many early game techs.  For example, they will always research a weapon, a defense, and life support.  They always want Trade as a tech, and will use it to send you freighters which will also extend their own "lives" as trade will slightly delay AIs from declaring war on them and conquering them.

Additionally, sometimes there is the event in which a minor race "steals" all the techs of a major AI race.  In DA, there will be the message that the minor AI wants to trade the techs for planets.  This is still bugged, as the AI will do no such thing.  However, if one declares war on that minor AI, sweeps away its vessels, and is poised to invade, that minor AI will trade many/all of those same techs in exchange for survival.  That tech windfall can be the difference in Suicidal games.

All AIs start off "knowing" where all inhabitable planets and mining anomalies are.  Major race AIs rush buy colony ships first, then constructors.  Since minor AIs cannot colonize, they start off rush buying constructors.  Hence, a player has a better chance of being first to mining anomalies when minor AIs are NOT in the game.  OTOH, minor race mining bases are ripe for vulturing.  Minor races allow some other somewhat gamey tactics, also.  When one has nine suicidal-level AIs in the game, one may become a bit more open-minded of such ploys!

I use the Tolmekkian mod with smart Minors.  It does make a difference.