You can make simple repairs and craft temporary items, not much more

RAW Tinker tools allow you to make small repairs, jury-rig a temporary replacement for stuff and do some archeology and damage investigations. Nothing else. There is nothing to suggest (aside from DM fiat) that it is capable of doing anything else.

The wind-up dragon in the image was probably made by a Rock Gnome utilising their Tinker trait:

You have proficiency with artisan’s tools (tinker’s tools). Using those tools, you can spend 1 hour and 10 gp worth of materials to construct a Tiny clockwork device (AC 5, 1 hp). The device ceases to function after 24 hours (unless you spend 1 hour repairing it to keep the device functioning), or when you use your action to dismantle it; at that time, you can reclaim the materials used to create it. You can have up to three such devices active at a time.

When you create a device, choose one of the following options:

Clockwork Toy. This toy is a clockwork animal, monster, or person, such as a frog, mouse, bird, dragon, or soldier. When placed on the ground, the toy moves 5 feet across the ground on each of your turns in a random direction. It makes noises as appropriate to the creature it represents.

I believe, that this racial trait's existence is an argument that normal proficiency in tinker's tools should not allow you to create such a clockwork toy, because it would make this trait irrelevant.

Another argument is existence of the Quicksmithing feat in the Plane Shift: Kaladesh PDF, one of the benefits of which is identical to the Rock Gnome's Tinker trait, including the ability to craft a clockwork toy dragon.

As for traps, there is a great difference between being able to disarm traps and being able to disarm traps without triggering it and being caught in it. The best trap defuser I've seen was a hasted raging barbarian with a warhammer. Few things could put a dent in him, and few things could continue to work after being bashed with a heavy slab of metal repeatedly.

Forgo isn't the best word choice, Assurance works as rolling

The clear intent of Assurance is that you no longer have to actually roll a die, but the results should be adjudicated as though you had. Anything that references "rolling a success" or similar is functionally the same as "getting a success" and Assurance affects either.

Normally I would take words at their face value, but we have to remember that Paizo has a number of writers and has adopted a stance that things don't have to be written exactly the same to mean the same thing (vis-à-vis "rolling" vs "getting"). And we know that Assurance is still a type of roll because it's a Fortune effect.

A fortune effect beneficially alters how you roll your dice. You can never have more than one fortune effect alter a single roll. If multiple fortune effects would apply, you have to pick which to use. If a fortune effect and a misfortune effect would apply to the same roll, the two cancel each other out, and you roll normally.

A fun side effect of this is that Assurance can be negated with a Misfortune effect and vice versa; if you have a Misfortune effect on you, you can use Assurance to roll normally.

Because Assurance is still a type of roll (even if there is no physical/digital rolling of a die), it qualifies for any text referencing rolling a [result] (assuming 10+proficiency is enough to succeed).