Please read this Hubert Plot Multiple marker in map using List. It discusses most of what you want to do (except storing information in a TinyDB). Read the information about the National Park tutorial that is mentioned to learn how to make a created Marker clickable.
Yes, you will have to make a List. I advise you not to use separate screens, or use your global place_lat and lon in the placedMarker. Initialize Screen. When you switch to that screen, the LocationSensor will most likely provide a location of 0,0 because it probably will not have yet obtained a satellite fix (that takes 20 to 40 seconds on most devices).
Consider reading and doing the two tutorials Using the Location Sensor if you have not already done so. Also, the Map component documentation is Map components
Your app is an ambitious Project for a new App Inventor 2 user . Here are some resources to help you learn to use the AI2 tools. A very good way to learn App Inventor is to read the free Inventor's Manual here in the AI2 free online eBook http://www.appinventor.org/book2 ... the links are at the bottom of the Web page. The book 'teaches' users how to program with AI2 blocks.
There is a free programming course here http://www.appinventor.org/content/CourseInABox/Intro and the aia files for the projects in the book are here: http://www.appinventor.org/bookFiles
How to do a lot of basic things with App Inventor are described here: http://www.appinventor.org/content/howDoYou/eventHandling .
Also look here http://kio4.com/appinventor/index.htm and here http://www.imagnity.com/tutorial-index/ for more tutorials.