If a space shuttle is going to crash during a botched landing back on earth, is there any possible way (emergency vessel, etc.?) for crew to eject and land safely away from the shuttle?
No. That was one of the design tradeoffs in the shuttle. It was reasoned that, except for the last few seconds before la good landing, ejection would be an instant death sentence anyways, whether the unlucky astronaut was torn apart by wind shear, burned up by friction, or asphyxiated. The evidence is that all three happened with the Columbia accident
Short answer is NO; not with the current design, and even if it was possible to add in escape capsules or some other ejection device, the chances are that your crew would never make it to them before complete destruction of the ship.
If we look at Challenger first, that ship blew up around 73 seconds after launch. It's highly doubtful that the crew felt a thing or knew what was going on before the ship exploded. Their reaction time to the event would have been as close to zero as can be imagined, and even an automated escape system could not have got them clear in time. It would have also greatly inhibited their ability to control the craft during flight, by the way.
As for Columbia, a stray heat tile fell off and struck the wing, and there is some evidence that the ship sensors were registering something wrong for around 12 seconds prior to the actual breakup of the ship. But they were travelling at more than mach 19; so fast that any form of ejection would have been extremely problematic, not to mention risky.
On top of that, the weight requirements would have meant less payload available in the ship, meaning that it's less commercially viable AND the ejection system still only provides a slight increase in surviveability. Ultimately if something goes wrong during reentry or landing, ejection or survival pods are unlikely to help. Hence, they were never designed into the system.
You talk about "a space shuttle" ...
Well, there was "the Space Shuttle" which generally refers to the NASA design which was actually used, a Soviet design that was never flown with people in it, and various other designs which got not even that far. Notably, the ESA design got modified to allow for greater pilot survival chances, which reduced the payload by quite a bit before the program got scuttled.
Here is a writeup about escape options for the NASA Shuttle, including parachutes to be used at 25,000 feet.
The idea of a crew escape capsule sounds viable in many but not all situations, but it would take a significant bite into the payload capacity.
This is something that was looked into heavily during the design of the Shuttle Program. however it was more considered for during launch than landing.
Its also worth noting that the Enterprise and Columbia were actually fitted with ejection seats, as these were both deisnged initially to be flown with only two crewmembers
Most of this information can be found here
But Simply put... the added weight of the ejection seats and the various systems and engineering to support them meant that it would have required too much extra trhust to acheive orbit when there was such a limited window to use them effectively.
The below link might be of use to you
Short answer: Yes: http://mfwright.com/shuttlejump.html
It depends on how your landing is botched. But if the Shuttle is in stable aerodynamic flight, the crew is able to bail out. This is the preferred option if for whatever reason the Shuttle can't reach a airstrip for a regular landing. Because the Shuttle has extremely steep final descent, a crash landing on ground or ditching in water has very low survival probability for the crew.
However, because the bailout is "manual", the Shuttle has to be slow enough and in stable flight for it to be a possible option. The crew has to be able to move from their seats to the hatch and jump off using the guide pole to get them to safe distance from the Shuttle. This is not something you can do at the last moment, or if your emergency otherwise requires immediate egress.