Regarding email attachments from gmail app on iphone
For PDF files, you can import into iBooks and simply access it from iBooks. From there you can also send the PDF as an attachment for someone else by clicking on share.

For other files, I think your best bet would be using the Google Drive app or iCloud in order to keep on viewing it on your phone. Another thing you can do is save the files in the notes app and then you can also view it and send it out from there.

For the 5S, I'm sure that you can use iBooks for PDF but I'm not 100% sure on if you can put other file types into notes (although I don't see why not).