[RPG] Can a player character create a cursed magic item on purpose

I don't recall anything in the existing manuals that allows a "simple" way to detect curses. I believe they were trying to make curses more interesting to play. So, from the rules view there is no easy way to know if an item is cursed except by trial an error (It adds drama!).

An easy way out would be to house rule a curse-detecting clause to a spell (identify, for example), in the sense that it would detect the negative effect of using the item.

Other ways are to hint it to player. Lore, like you said, is a good approach. Legends, rumors, hystorical records could point to a certain object being cursed. Maybe there's a warning in the item's resting place or the PC sense something "not right" when they touch it.

The fact is that by allowing to easily detect a curse it cuts off a bit the point of it being cursed. Curses are meant to be narrative devices. If you want to avoid the hassle you can always reduce the "curse" to negative traits or flaw like the DMG suggest in the artifact section.

2000gp/day

The feat only gives a very short description of the item creation rules, and then refers the reader to the actual rules:

Benefit: You can create a wide variety of magic wondrous items. Crafting a wondrous item takes 1 day for each 1,000 gp in its price. To create a wondrous item, you must use up raw materials costing half of its base price. See the magic item creation rules in Magic Items for more information.

The magic item creation rules are authorative and supersede the feat description. The "1 day per 1000 gp" rule is merely a convenient combination of the "8 hours per day", and "1 hour per 1000 gp" rules for the sake of brevity. Since the magic item creation rules state that accelerated crafting reduces the time spent to 4 hours per 1000 gp, but does not touch on the 8 hour daily limit, there is no reason to assume that the daily crafting time limit is suddenly reduced to 4 hours.