[RPG] How do tinker’s tools interact with the ability to disarm traps

RAW the Rogue does receive the benefits of Expertise to his passive.

A passive check is a special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster. Here’s how to determine a character’s total for a passive check: 10 + all modifiers that normally apply to the check. - Player's Handbook P.174

The player has invested in making this character good at this, this is not a bad thing.

Rogues in general are supposed to be good at this type of thing, hence the proficiency bonus class feature and the player specifically spent a feat on making his passive perception better. The player could've spent this on another feat to specialize in another area (or gain a combat ability). This is a good thing, while it may make it difficult for the Rogue to be surprised by a trap or an ambush you should in no way try to outmaneuver this.

Don't worry, there are downsides to the Rogue for this.

To reliably spot traps and ambushes the rogue will need to be at the head of the marching order so that he has clear sight lines. Rogue's are not particularly hardy and the party as a whole is inviting more risk for this reward. Likewise while he is extremely excellent at spotting physical dangers, the Rogue will not be able to detect magic wards and other dangerous enchantments and may equally blunder into them.

Ways to handle his detection of a trap or an ambush

You are correct in assuming that only that PC has seen the trap/enemy. Unless he has some mode of telepathic communication he will need to speak out and announce the threat to everyone. The best way to handle this sort of thing is to pass notes or send text messages to the player(s) able to see/detect the issue and leave it to them to react and tell someone else. Intelligent enemies will see/hear the rogue warning the party and the combat should start immediately (no surprise round though).

The PC does not become omniscient of the trap upon detecting it.

The PHB itself is very, very vague on what information is received when a PC detects a trap. However, the DMG does have a nice little section about traps, their detection, and disarming them:

If the adventurers detect a trap before triggering it, they might be able to disarm it, either permanently or long enough to move past it. You might call for an Intelligence (Investigation) check for a character to deduce what needs to be done, followed by a Dexterity check using thieves' tools to perform the necessary sabotage...

...In most cases, a trap's description is clear enough that you can adjudicate whether a character's actions locate or foil the trap. As with many situations, you shouldn't allow die rolling to override clever play and good planning...

...Foiling traps can be a little more complicated. Consider a trapped treasure chest. If the chest is opened without first pulling on the two handles set in its sides, a mechanism inside fires a hail of poison needles toward anyone in front of it. After inspecting the chest and making a few checks, the characters are still unsure if it's trapped. Rather than simply open the chest, they prop a shield in front of it and push the chest open at a distance with an iron rod. In this case, the trap still triggers, but the hail of needles fires harmlessly into the shield. - Dungeon Master's Guide p. 121

Essentially though whether trap disarming is simply a dex check, a series of checks, and/or involves serious RP is up to you as a DM. I would encourage the open-ended approach the book suggests as it adds complexity and makes trap checking and disarming a more engaging process. Sitdown with the party OOC and discuss what the table as a whole thinks should happen for trap checks and move forward based on that consensus.

If you are talking about the Tinker's Tools found in the players hand book, then I don't think you need to worry. The tools themselves don't seem to be defined in the book, but the rock gnome tinker ability lists some things you can make with them. In particular, they're tiny, clockwork, gadgets, so it seems reasonable to assume that tinker's tools specifically refer to the tools you'd need to work with small mechanical devices, rather than large vehicles or fabrics.

More generally, just because the players can envision how to build something does not mean the characters can. Things like planes and, to a lesser extent, parachutes require a specialized knowledge of physics to get right and there's no reason to assume the characters would have this knowledge, even the wizards. What's more, in a world where dragons and griffons can fly, it's perfectly possible that traditional aeronautic devices, like planes from our world, simply wouldn't function.

You're perfectly in your right as DM to say "No, you can't build that thing." That said, you should endeavor to give them both the in-character reasons "Those aren't actually the right tools, physics doesn't work that way in this world, and your character has no reason to think this would work" and the out of character reasons "I'm worried this will cause balance problems and make it hard for me to run a good campaign for you." If you only tell them the in character reasons then the players will, naturally, view your reasons as obstacles to overcome, rather than a request to stop trying. On the other hand, an out of game request won't cause any confusion, but in game reasons can make it go over better and are nice to have regardless.

If one of your players really wants to play a character who can build anything via mundane means, you could try working with them to find or make a class that focuses on just that and only builds level appropriate things in reasonable quantities (this means both not being able to build a bi-plane at level one and being able to build a jet pack when everyone else is getting flight spells).