1 a phone is ringing.
You mean like there s a phone ringing but you dont know which one or where is it? If so, you can say: 有电话在响。However if what you really meant is THE phone is ringing, you can say: 电话在响。Last but not least, if you meant the phone starts to ring, you can say: 电话响了。 All very similar, but with subtle differences.
2 finding a new job
找一份新工作 or simly as 找新工作。
3 I learn how to cook - doesnt make any sense!
either you learned how to cook, 我学会了做饭
or you are learning how to cook 我正在学做饭
or you want to learn how to cook, 我想学做饭
which one of them do you mean?