Yes. Depending on the strength of the time dilation, a repair may not be possible to complete before the journey is over.

But anyone capable of getting a ship near lightspeed would also have the physics and math knowledge necessary to calculate their level of time dilation, so they could make logical decisions regarding necessary repairs.

In theory, exactly the same as any other spaceship.

Anyone attempting repairs is operating in the same inertial reference as the ship, so from their perspective it's no different from repairing a ship at any other speed.

Time dilation as you approach the speed of light is not speculation, it's fact. Time slows down heavily the closer you approach lightspeed and does not pass at all for anything that can actually reach it.

Any discussion of matter going the speed of light is speculation, because it is impossible in our current understanding of physics.

In this scenario the ship is moving at the speed of light so it is not experiencing time, just like the people inside it.

It cannot breakdown while moving at lightspeed, because no time can pass to allow failures to occur.

But matter can't actually go the speed of light, only energy can, so this is all just a fun thought exercise.

The faster you travel, the more time dilates. At the speed of light, time does not move at all.

From an outside observers perspective it would take 100 years. For anyone on the ship it would be instantaneous, if you assume no acceleration or deceleration period.