The items that are laying in the open like alchemical ingredients, ingots, etc....do they respawn after time ? I know dungeons and other places do but I want to know if I take these things that aren't in chests and in my home ,will they come back?

Probably. If you stay out of Solitude for 30 game days.

Does anyone know for sure?

All player houses use encounter zones that guarantee they never reset naturally. It is, however, possible to force a respawn with the "ResetInterior" console command.

Interesting. I don't use the "paid for" player houses any more now that there are some really great mods for player housing.... I never "pick" anything no matter where, since I despise alchemy and none of the bits are worth much gold - but thought the houses in vanilla might follow the "out of cell 30 day respawn" thing.

Yea that is disappointing if true. I'm console so no force respawn for me. I'm gonna leave them because they decorate the house and it would look dumb if everything were permanently bare. I can't even place items as decoration in fear of them disappearing....