Is it safe to keep the GPU on 100% utilization for a very long time?
Short answer: This should be safe on well-designed hardware.
Long answer: The GPU (and its software environment: drivers, OS, daemons) are designed to protect from overheating - the GPU should first turn the fans to a higher RPM, if that can't keep a safe temperature then the GPU throttles the workload (usually by reducing the clock frequency). This will assure a heat profile that will not damage the GPU and thus not the PC (or the room).
Caveat: There exist cheap knock-off graphic cards, where the firmware is specifically designed to sacrifice safety for performance. While I don't think those exist for a 1050, I am not 100% sure. You should also prefer the Nvidia drivers downloaded from their website over "optimized" vendor drivers, which might do the same thing.
A house fire is extremely unlikely, but the lifespan of the card may be reduced.
Long-term overheating of the GPU chip probably won't start a fire. The chip may deteriorate and start misbehaving or die completely, but silicon chips aren't too flammable. Bad things usually happen when electrolytic capacitors fail and blow up, but these won't be subject to overheating just because the card is doing a lot of crunching and you also hopefully have a metal PC case to contain the hot shrapnel that results from such failures.
However, consumer-grade parts aren't in general designed for long-term 24/7 loads. It is thus fairly likely that the card will die sooner than if it wasn't subject to such loads. It is hard to say how much sooner without having some more statistics on a given model. Some people in the HPC community advocate using high-end gaming GPUs instead of special HPC compute parts, and there seems to be some economical sense in that. Although the commodity parts die in a year or so, it's cheaper to keep replacing them because they're many times cheaper than the alternative
Yes, the card is likely to wear out sooner if it is under constant load. At small geometries, Electromigration is a significant source of device failures, and devices will typically be designed with a specific target lifetime in mind. This might be generous for typical operation (e.g. 5 years continuous operation), but might not assume 100% maximum operating point for all of that time. As soon as you start over-clocking, you can expect that target to reduce significantly. (Equally, running at only 80% load would maybe double the lifetime due to this failure mechanism).
There are of course other failures which relate to running components hot, or thermal cycling, this is just to point out that modern electronics (and even 1980's electronics when badly designed) can be suceptible to 'wearing out'.