If its a screwtop bottle, will be ok for couple weeks or so. If a cork should be drunk within 2 days.
Any "leftover" wine can always be used in cooking.
Absolutely no difference between a screwcap or a cork I'm afraid.
Once opened the wine becomes exposed to the oxygen in our atmosphere and slowly starts to oxydize which will impair the taste. However it should not affect it too much for the first couple of days.
I have one of those vacuvin thingys that seems to work very well although I only usually need it overnight
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