How to perform QA in agile scrum sprints? How does testing happens when developers are developing on last day of sprint?

Look to adapt agile scrum for a small software development team. Needs some clarification on the overall process. If we decide to go with 2 weeks sprint 10 working days. 8 hours per day per resource

For designer we plan to keep them one sprint ahead so developers have everything they need from design side when they start their sprint. Now their time is divided between R&D, Meetings, Development and Unit testing. Roughly 5-6 hours daily for development. and rest for meetings and unit testing as needed.

How does QA operates? Is is necessary to have nightly builds and pass that on to QA? if not whats recommended? How are bugs handled? should we set aside time withing the same sprint for bugs or handle them in next sprint? Now if developers are developing daily, how does testing happens for stuff developed on the last day of sprint or no development should happen on last day? does testing carry over to next sprint? How to do the release plan? it is usual practice to release right after sprint or release work ahead 1-2 sprints? Where does documentation fits in? Is it part of the sprint or next sprint for items developed and tested in previous sprint?

Initial thoughts are to design 1-2 sprint ahead, develop and test within sprint, carry over untested stuff (not sure how to track the sprint KPI then), take next sprint to test and do documentation and then do the release once all ready? Is this right approach?

Thank in advance.