would a standard prism work for rgb?

[Julian95]

yes you can do it but you need to make or buy a very precise aligning system for it to produce a high quality combined output

 

[Cyparagon]

What if 2 or more prisms are installed in sequence - would it increase the angle?

Yes, it would increase the angle by about 2, but it would be 10 times harder to align. There are better options.

What if prism material would have higher refraction index than glass - would it increase the angle?

Yes, it would increase the angle proportionally, but it would be about 10 times more expensive to purchase. There are better options.

 

[Benm]

Indeed. The reason to use things like dichro's instead of ordinary prisms is mostly a practical one. Even with materials with higher refractive indices the whole setup would be impractically large to transport, and be sensitive to thermal expansion of all materials used possibly requiring re-alignment for every time you use it.

So in short: Yes, you can use ordinary prisms to combine 3 laser beams into a while one, but it would just not be overly practical. If you want to do this for a science project, museum demonstration or something like that, proceed.