Nepal Airlines is held accountable to many other airlines. Airlines are actually very safe in comparison to other modes of travel such as car, or public transportation. One incident can taint an institution with bad first impressions however an incident could just as easily occur within a different airline. It is possible it was mere chance that tainted Nepal Airline's reputation.
Yes, Nepal Airlines are likely to be as safe as any other airline. The plane that recently crashed was brand new and was flying in clear weather. It is therefore unlikely that the problem that caused the crash is systemic. Since the pilot noticed a mechanical error right before the crash I would guess that the specific type of plane should be avoided, not the airline.
No, I do not believe Nepal Airlines is either safe or trustworthy. Scattered reports of the company's unexplained accidents or crashes seem to hit the headlines every few years, and rumors about dishonesty and even fraud cloud Nepal Airlines' history. Perhaps the reports are exaggerated, but an airline is not a typical business that can absorb its losses and move on; human lives depend on the safety of the planes, and if there is even a shadow of a doubt about the company, it is better to be safe than to be sorry.
According to recent reports, Nepal Airlines is among the firms listed with poor safety ratings. It may be because of the geography of the region and not the company itself. The airline likely does what it can to keep passengers safe. However, the terrain that the planes fly through is treacherous, making Nepal Airlines less safe than other commercial airlines.