1/4 inch per foot.
That would depend on the height of the drain and how deep the sink is. As long as the drain is lower than the bottom of the sink, it should be fine.
They should not be cleaned in the kitchen sink and YES, it will harden in the drain.
You have a blockage in your main sewerline. You have a problem with your venting system. This is why some codes now require a vent within 6" of the toilet. If you will add a vvent to your main line at the toilet you will stop this. Check to make sure your vents are not clogged by a bird or bees nest first.
Kitchen sink and washer use same drain line. Drain line clogged causing backup of drainage from washer into kitchen sink. Have drain line unclogged to take care of problem. If drain line not clogged, check for proper venting of drain lines.
Maybe 600 for a kitchen sink to be installed.
yes.
By properly sizing the vent by fixture units and developed lengh and pitching it up from the fixture it serves
The overflow is built into the sink, it is not part of the drain. If there is no overflow, you can not add it.
That's possible but difficult and seemingly unnecessary. Why not just lead it's drain to the garden or to perimeter drain.
To install black kitchen sinks into one's home, one needs to purchase a black kitchen sink from stores such as B&Q. One then needs a plumbing expert to install the sink correctly.
no