Is the following publishing strategy convenient? I work in the field of CS, and recently published one of my works (Algorithm A) in arXiv (not peer-reviewed), as a short technical report which introduces a new method along with relevant mathematical analysis/proofs/etc. 

I want to submit a paper-X to a conference by using that method in some practical applications and in combination with other methods. I decided to not introduce Algorithm A in that work due to space limits and enough contributions that paper-X has by itself. 

But i want to also submit an extended version of paper-X to a journal along with introducing Algorithm A with proper further analysis/proofs.

So:

1- Is this allowed?

2- Is it convenient / advised?
As you describe it, it seems like standard practice (more or less). Conferences prefer somewhat shorter works than journals due to time (reviewing) and space (proceedings) considerations. Journals don't have that limitation, though some won't publish long works. 

You will need to be careful about citations of your own work, of course and you may have issues with the possibility of double-blind review in some situations. 

However, if you publish the journal article first, there would probably be a presumption by the conference committee that it is "old work" and not suitable. But, in general, extending an older work is acceptable - even praiseworthy. 

But, to satisfy journal reviewers, the "extended" work should be more than a restating of the earlier work. A summary of older work might not be enough, even if it brings together the, already published, algorithm, and the, already published, use. Reviewers may be looking for what is new.