Hi, I just wanted to know if it is possible to just install the frappe framework and then install the necessary modules from ERPNext as apps. If yes, how can it be done? Thank you.
you can’t pick and choose which module in Erpnext to be installed; However, you can hide modules that you don’t require. Also you only have access to modules that you have permission to, so that means you can also hide modules using permissions.
https://frappe.github.io/erpnext/user/manual/en/customize-erpnext/articles/module-visibility
https://frappe.github.io/erpnext/user/manual/en/customize-erpnext/hiding-modules-and-features
Thank you for your answer. Can I add custom made modules to ERPNext locally? Which is a better choice to write custome modules, working on top of ERPNext or straight from Frappe framework?
If you want to customize ErpNext modules themselves, then your best option is to put your cosumization in custom app then you just export fixtures.
If you wanna create your own new modules, the you just create frappe app and use hooks.
I recommend since you are interested in development, to go through Frappe Developer Tutorial before you posting your general questions here. because all these questions are already answered in the documentation 
http://frappe.github.io/frappe/user/en/