The belt or transmission is likely the problem. Could also be the pump belt if it's one that has a belt, or even debris in the pump intake. - Call an appliance tech, it's an easy fix UNLESS it's the transmission.
You can drain it directly into a drain pipe. Just make sure the the top of the drain pipe is even with the top of the washing machine. If not, the water from the washing machine will drain all of the time. There is no valve in the machine to stop the water from draining. The washing machine drains using a pump motor.
No.
Draining refers to water falling due to gravity so you can't technically drain a washing machine to an overhead drain. However, washing machines don't really drain. The water is pumped out and up and can therefore be discharged to a drain that is slightly higher than the washing machine itself
yes
No, stand pipe for washing machine is meant only for washing machine. Tie sink into drain line that washing machine stand pipe is tied into. 2" minimum drain line should be what you tie into. Sink drain line use 1 1/2".
......before, but I would not recommend direct drain. The washing machine hose must extend up above the flood rim of the washing machine before entering the drain. If not, there is a possibility of sewage backing up into your washing machine.
yes
yes
to push any button .
no, in fact most plumbing codes require a 2" drain/trap for washing maching drain.
The drain is getting plugged and the toilet is lower than the washing machine drain so it is easier for the water to come up in the toilet than to go straight out the drain. Put some drain cleaner down the drain where the washing machine drains and that may solve the problem.
2" minimum.