The red one is something in the Oncidium alliance (it's likely impossible to get a further ID unless it came with the plant). It's probably ok to repot this one (maybe once it's done blooming).
The other is in the Catasetum alliance – there's lots of good info in the Catasetum/Stanhopea subforum, (and also many knowledgeable members). Sunset Valley Orchids is also an invaluable source of information on growing Catasetum/related genera and intergenerics. Regarding the spots, I don't think they're anything to worry about, and since this orchid will drop its leaves later this season, it's not a big deal. Right now it's in its active growth season (as opposed to its dormant season) – this is when it's growing lots of new roots and leaves. You don't want to repot this one right now, since it's actively growing; wait until it enters dormancy (it'll lose its leaves), and you can repot then if you feel that it's necessary.
Repotting a Phal might cause some buds to blast and cause its flowers to drop faster, so unless its potting conditions might contribute to disease, you may want to wait (although you'll see blooms next year anyway).
Hope this helps.