If you don't have SSMS installed, I would recommend that you install and download it. Without SSMS, or some other query tool, administering a database is difficult. But there is a query editor in the Azure portal.
There is no predefined role db_writer, but there is a predefined db_datawriter. Membership in that role gives the user rights to insert, update and delete data in tables. However, you talk about other users being able to create web apps. The web apps themselves are created elsewhere, but possibly web app developers wants to create tables and stored procedures. Permission to do that does not follow with db_datawriter.
To that end, I recommend that you do:
CREATE ROLE my_ddladmin
ALTER MEMBER db_ddladmin ADD MEMBER my_ddladmin
DENY ALTER ANY DATABASE DDL TRIGGER TO my_ddladmin
Then you add developers to the role my_ddladmin.
That is, the predefined role db_ddladmin gives users rights to create stored procedures, tables etc. Unfortunately, it also gives them permission to deal with DDL triggers, something which should reserved for the database owner. This is why I recommend that you to create your own role.
Note that membership in db_ddladmin, does not give permission to change data in tables, so developers also need membership in db_ddladmin.