There are thousands of miles of high speed railway, with a good safety record.
Nothing is absolutely safe, but rail is certainly safer than road transport, and high speed lines seem at least as safe as lower speed ones since they are better built and often have fewer oportunities for acces by animals and vehicles.
No one knows what the absolute limiting speed is for more or less conventional railways, but about 300MPH has been suggested.
Beyond about 300MPH the energy and other costs start to become similar to the costs of flying rendering the idea not actualy impossible, but a bit pointless.
I have no doubt that 300MPH will eventualy be exceeded for test or record breaking purposes, but rather doubt that we will ever see regular operation at much more than 300MPH.
Still higher speeds could be achieved with maglev and linear motor drive, but is not really conventional high speed railway.
The ultimate speed limit for any ground transport system is the speed of sound which is about 750MPH, higher speeds could be achieved but would not be reaslistic on account of sonic booms. High flying supersonic aircraft are bad enough, imagine that a ground level.