Google Cloud: Do we need a compute engine to run a deployed python code?
We need more information and see some code to be able to help you better but in general the work you describe should be able to get done via http and you don't need any special C libraries, hence you could go with appengine and create task queues for your jobs. 
Be prepared that using only appengine can be trickier than having an operating system that you can leverage. There is no operating system with appengine once you've deployed, you must use only the functionality supplied in appengine. 
But yes, as far as I can tell from the information you provide, an appengine app should be able to do the work you describe. Try writing some code, deploy the appengine app and get back here and ask if you have specific trouble. 
You can always add compute engine to your appengine project if you need it later.
Sorry, I don't really have much technical background and I know it sounds like a confused question. However, I will try my best to explain what I want to do in here.
My daily routine tasks involved lots of digital marketing data (very large data >20GB+) from different types of platform. As you can see, when I try to analyze these data, I need to aggregate these data into a similar format. The tedious part of my job is it normally involved lots of manual downloads, lots of data cleansing, and lots of upload(I upload the cleaned data to Google Cloud Storage so I can use BigQuery!).
I feel do these tasks manually are extremely inefficient, and I think the only logical choice is automate these tasks on Google Cloud Platform.
After months of effort, I am managed to do these tasks in semi-auto fashion, which I wrote some python programs and make a schtask batch for following:

Download (A python program makes API calls to download platform data to my local drive)
Cleansing (A python program cleansing these data locally) 
Upload to Cloud Storage (A python program upload "cleaned" data using gsutil)

Although, it saved lots of my time, but everything is still done locally on my desktop PC.
Here are my real questions, I am sure there is a way to manage all these tasks (download, cleansing, upload) in Google Cloud without touching my local PC, where should I start?

How can I run these Python program on Google Cloud? I know that I can deploy these Python programs in App Engine, however, to allow these program to do their jobs, do I also need a compute engine? or simple deployment would do the job?
How do I schtask for these apps on Google Cloud?
I know Cloud Storage is only one of many ways to store the data on GCP, since I have these data from different types of platform, and they are all in different formats and metrics. So what would be the best way to store these data efficiently on Google Cloud? CloudSQL, Datastore or BigTable?

Thanks!