Yes, that first one is a Dendrobium - looks like a "Phal" type (Phalaenthe section of Dendrobium). The second looks like a Vanda, or related.
As far as I know, neither will rebloom on old spikes, so you can cut the spikes when the blooms are done - I wait for the spikes to be brown and dry, but I know others go ahead and cut them before then. Just cut as far down as you can without damaging the plant - where you cut the spike does not have any affect on the plant, except in the case of plants that can rebloom on previously bloomed spikes.
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