1) No, items spawn once a day at 00:00 TCT. If you were active and went to the city at least once in the 24 hours prior, there is a chance items spawn. You can increase your odds with merits or certain company perks. Without a 3rd party app, you do need to zoom in a little bit in order to see items. This does not change whether they are there or not though.
2) No, items will stay on the map until you collect them.
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