This depends strongly on your DM's personality.
Remember, everyone is playing tabletop games to have fun together, so if something is happening to dampen your fun, it's completely reasonable to bring that up, but keep in mind you don't want to ruin the DM's/everyone else's fun while you're at it. It sounds like you understand this ("I don't want to be that guy"), but I assure you that your experience matters too -- the "everyone" includes you -- so don't feel bad bringing it up, just make sure you do it tactfully.
Sadly, it's hard to advise you how to make your feedback land well. Some people are quite sensitive to feedback and take even gentle constructive criticism personally. Some people are completely aloof to feedback from others and take neither negative nor constructive criticism seriously. Since I don't know your DM personally, I can't recommend a specific tone or amount of criticism and feedback appropriate to your table. You'll have to use your own judgement there. What I can offer is some general advice for tabletop conflict resolution based on what you've written here.
Session Zero and You
We never really had a session 0
You should have.
The best time for Session Zero was before dice ever hit the table. The second-best time is right now. I cannot stress this enough, but I will never stop trying! Approach your DM and party and say something like "Hey guys, I realized we never really talked about house rules and expectations for this game! I know we already started, but we should still do that. When is good for you guys? Maybe before we start up next session?" You can just use the phrase "Session Zero" if your group is familiar. This gives you the opportunity to bring up these things that have been bugging you (as gently as is appropriate for your DM's personality, in your judgement), and hopefully prevent others from cropping up in the future!
They use saving throws and skill checks somewhat interchangeably (and did not know what saving throws were until our last session)
This will improve naturally over time. You can offer small corrections in the moment quickly without derailing the game. For example, when the DM says "make a charisma save" when a PC is trying to convince someone something, just say "you mean a charisma check, right?"
In combat, they seldom get us to roll for initiative/have a set turn order, which sometimes results in some players doing stuff twice before another has their turn
Everyone gets a turn (barring conditions etc). This is a fundamental rule of combat. It's not "my guy" syndrome for you to expect to have a turn every round, and this is something you should firmly clarify ASAP. Frankly I'm surprised no one spoke up about this immediately. Unless you fancy an ongoing game where people are skipped over and action economy is totally arbitrary, don't take no for an answer on this one.
If your DM needs convincing, remind them that having high dex feels less useful when you don't get one of the primary benefits of going fast (not to mention the various other ways you may have improved your initiative bonus), and it's extremely unfair to skip someone's turn entirely.
In their last campaign in this world, they felt like there was too much narrative and not enough dice-rolling, and it feels like they have overcompensated for this; during our last session most of us were sitting twiddling our thumbs for half an hour while the bard bluffing his way past the king's advisors in a lengthy conversation was rolling for Charisma every second sentence.
Others have already suggested great choices here. Just matter-of-factly point out that it's not particularly fun to sit and watch one character roll the same check for 20 minutes with nothing to do yourself. You could introduce your DM to the idea of skill challenges a la 4E, or just kindly ask for more inclusion of the rest of the party in future social encounters.
They can sometimes let the players dictate which skill they roll a check for when performing an action, eg a player will say "I want to roll an Arcana check on this amulet to check for magic"
Personally I don't see the issue here. Ultimately, it's up to the DM to decide if a check succeeds or fails, and even what checks a PC should make at all. Allowing players to suggest which skill they would like to use to solve a given problem encourages creative thinking and can make for more interesting solutions than the DM may have had in mind. It's hardly a dictation on the player's part, but perhaps your DM needs a reminder of that? If instead it is coming from a place of power-gaming from the other players, this is yet another reason to host a Session Zero ASAP.
In Conclusion, or, TL;DR
Have an open, honest conversation with your DM and fellow players about the things that are bothering you (especially the initiative thing). Game knowledge will come with time, and you can help along the way. Remember: the goal is for everyone, you included, to have fun together!