Hi Avi,
First off - have to give the plug: you can avoid much of the need to copy and paste sources at at by using our Source Sheet builder:
www.sefaria.org/sheets
You can copy and paste the normal way in our reader app as well, although there are some issues. In particular you can't really copy the bilingual view at once, you'll need to copy hebrew and english separately.
If you click on any piece of text you'll see a (+) button appear. This also has an option to "Copy to Clipboard.." which will bring up a version of the selected text without any weird formatting, in English and Hebrew. If you want to copy a range of text on the page, first click on the beginning line, then click on the ending line to highlight a range.
We're currently working on some big redesigns which will make this process much simpler. Stay tuned!
Thanks,
Brett