1、The first "都" is redundant and I don't think it will be used in any normal expressions.The second "都" in this sentence suggests that instead of mentioning one or two aspects only,you'd better report your activities with all the details during this period.What's more,it also emphasized the statement.However,I'm not sure if it's necessary.
2、Plz note that "下雨 起来" is not same as "下起雨来" cuz the former expression simply means "raining"+"get up",and it is less common to put them together.Another expression "下起雨来" is correct,just like saying "it's rainning now"(下雨了).