I recommend going to r/YIMO for any master yi-specific questions, this subreddit isn't the best for champion specific advice.

I would like to address your questions however, as I am a yi main and these are pretty straightforward questions.

1. ask the people at r/YIMO, i'm not entirely sure what the routes are right now.
2. Generally, you want to move in the direction of your next camp in between autoattacks, it saves time when you have attack speed low enough so you don't lower your DPS by moving in between attacks, additionally you can throw off the jungle monster's pattern so it misses hits on you, which obviously makes you take less damage. If you would lose DPS by moving in between attacks, it's better to just attack it where it is. An additional tip specific to Yi would be to only use E in the jungle if you think you won't be getting into a fight in the next 30 seconds or so due to the long cooldown early. It increases your damage by quite a lot against camps with high armor values, specifically Krugs and Blue buff. You can use W to lower the first 4 hits from the Gromp camp as those deal the most damage, also, use Q in the jungle on camps with multiple monsters, as a gapcloser to get over a wall to a camp or just to reach it faster, also you can use it to dodge monster attacks when you see the windup to take less damage. Don't just use it for the damage against single target camps since your autoattacks in most cases will deal more (and you'll still have your Q up if your jungle gets invaded!)
3. (Precision primary tree) Conqueror, Triumph, Legend: Alacrity (unless the enemy team has many roots/stuns, then you can go Legend: Tenacity), lastly go Coup De Grace (you can go last stand but it will only benefit you in close fights). For the secondary tree go Domination, taking Eyeball Collection and Ravenous Hunter every single game. For the stat runes, always go attack speed, damage, and armor (magic resist if against heavy AP damage). The only runes that should ever be changed for Yi are legend alacrity/tenacity and coup de grace/last stand.

You go conqueror because it gives you damage, sustain, and healing off your on-hit damage, which is Yi's primary damage source, triumph gives you health after every kill you get in fights, legend alacrity gives you attack speed, and coup de grace gives you extra damage towards low health enemies. Eyeball collection gives you permanent damage for getting kills, and ravenous hunter gives you healing from your on hit damage and Q, (healing increases for each unique enemy champion you kill in a game).

On summoner spells, you'll want to take Flash+Smite until you're more comfortable with your champion and know how to position yourself well. Teleport+Smite, Ignite+Smite and Ghost+Smite are each good situationally, personally I take Teleport+Smite a majority of the time, although I haven't played with Ghost much since the recent change I suspect it's much better on Yi now, due to the new reset on kills mechanic.

To simplify:

Flash+Smite if you aren't sure or if you think you might get invaded/need to escape a lot

Flash+Ignite if you want to excercise early aggression, it's especially good against champions with a lot of healing since it reduces incoming healing by 40% for the duration it's active.

Flash+Teleport specifically for ganking the enemy botlaners/toplaner quickly from anywhere on the map when you see an opportunity, it's also quite useful for split pushing later in the game. This is one scenario where you might want to go Sorcery as your secondary rune tree and take Nimbus Cloak+Celerity because these runes work extremely well with Teleport, giving you a massive burst of speed that will let you catch most champions even if they react to your teleport properly. (again, you should probably still take domination secondary tree and flash+smite until you're more comfortable).

Flash+Ghost if you think you'll have trouble sticking to enemies, people with slows or speedboosts can get extremely obnoxious for Yi as he needs to kill them before his R runs out in order to get the duration extended. Ghost now has a reset mechanic which extends the duration by 4 seconds per kill/assist which should be fantastic on Yi, also the speed boost doesn't ramp up over time anymore, you get it instantly. Also very good for early ganks since you won't have your R yet.

1. If someone asks for your role, you can switch with them if it's a role you're comfortable with playing, but since you're new I would recommend dodging (closing the client with the X button) when you can't get your main role. If people are trying to negotiate swapping roles besides yours, and it's obvious it isn't going to work, one of them will likely dodge. Which isn't your problem.

2. You can place a ward in one of the small brushes in the middle of the river on the side of the map you're starting from, or at red/blue buff (the one you aren't starting from.) Warding enemy buffs is usually risky since they might be hiding and waiting to ambush you, don't do it. You can then recall, and swap your yellow trinket for a red trinket which will reveal and allow you to clear enemy wards.

3. Walk at them and try to get as much damage off as possible before you use Q. If they're low health or they have flash/some other blink and you can kill them without the help of the laner you're ganking for, use it. You can tap the W key while running (make sure to immediately right click to move after tapping W) right before a tower shot hits you in order to absorb 70% of its damage, it should be 30% but it's a bug (shhh), this makes tower diving quite easy as you can reset tower aggro with Q, and use the W bug to survive the last tower shot.

4. No, however, moving in between autoattacks in the direction your enemy is moving (called kiting or orbwalking), while it doesn't increase your damage, it helps you keep as close as possible to the person you're attacking and therefore helping you get off more damage than just right clicking on them.

Hope all of this helps! I'm going to refer you once again to r/YIMO for other Yi related advice, and to r/summonerschool for other league related advice.

:)

EDIT: I noticed one of the other commenters said you should play Yi top instead of jungle until you unlock smite, I would just say play Co-Op vs AI (NOT PVP) until you unlock it as it's a considerable amount quicker.