Welcome to the forum!
By Shelob "Red Spider", that's only the hybrid name, so I guess the genus name is miltassia (mtssa), a type of oncidium intergeneric. And And the Supersuk "Eureka"... should be a paphiopedilum (paph), I think.
When orchids are moved, stress can cause flowers to abort prematurely and buds to blast because conditions are changed. Unless the orchids have bad roots, it shouldn't be a worry as sometimes orchids shed buds/flowers when brought home. Once a bud is wilting, it usually means it's a goner, but don't get hopeless, because there may be a tiny chance for plumping, or even if you lose it, it'll bloom in the future!
It's okay for old leaves to brown and fall off. If tips are brown, then it may be overfertilized. If brown occurs in patches, it can be sunburn, fungus, harmless leaf spot, or virus.
Please check the FAQs for more info!
Find the green box and click oncidium or paphiopedilum! Good luck!