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Have you tried cleaning the aerators on the affected faucets?
An aerator is on the end of a faucet spout. You just unscrew it and clean out the sediment which can reduce the flow significantly.
Ok, it wasn't clear to me this was hot water only. How many handles does the basement shower have?
I'm referring to the shower valve/faucet
If the shower has a single handle then the cartridge in the shower valve will probably need to be replaced. Kitchen sinks can have 1 or 2 handles. The side sprayer problem is most likely due to a problem with the diverter in the faucet. If the flow out of the spout is poor just on the hot side then the hot side of the faucet could be clogged. It could be in the faucet it self or possibly the washer in the shut off under the sink could have broken loose and is restricting the flow. I'd need the brand and model of either faucet to give you specifics.
You won't find the info on the faucets. If you don't have the invoice(s) or know the model a picture might help. I'm online until ~7 pm EDT (I do take breaks) I'll respond as soon as I can. I need the models or pics before I can give you any model specific info.
What happened? Do you still need help with this?