Question: Is it true that its compulsory to dry your private parts after doing istinja?
Answer: No, it is optional.
Question: If I wash my childrens clothes with my clothes((That I pray in)) in the washing machine , will my clothes then become impure if they had some najis on them?
Answer: Not if the water is changed by the machine several times. 4 times would be enough. However, you shouldn't mix clothes that you know for sure have najis on them with items that are without najis, because on the first wash this will make the pure items najis for no reason.
Question: Are washing machines or plastic tubs considered najis if you have previously washed something impure in them?
Answer: If one washed something with najis that doesn't have a trace on it, it is enough to wash the item three times with different water and wringing each time. After taking the item out and wringing it well the 3rd time it is tahir. However, the tub needs to be washed 1 more time with water.
Question: I have been trying now to use my left hand for istinja, but I can't seem to reach the back area and clean myself properly with my left hand , so I then finish off with my right hand, is it only makrooh or haram to use the right hand, since I know I wasnt able to clean properly with my left?
Answer: It is neither makruuh nor haraam if you can't manage to remove all the najis with your left, but you should learn how as soon as you can.
... and Allah knows best.