Yes, this is possible. Fist you need an adapter from the lens mount of the Panasonic Lumix DMC to T2 (something like this: TS-Optics-T2-Adapterring-fuer-Micro-Four-Thirds-Bajonett).
For eyepiece projection you then need an adapter where you can insert your eyepiece and connect the T2 mount from the other adapter (something like this: TS-Optics Adapter for Eyepiece Projection and Focal Photography)
I am not aware of a solution for 2" eyepieces, but this should work fine for 1.25". You can also connect the camera directly to the telescope without an eyepiece, in which case the telescope works like a camera lens of focal length f=650mm, without the additional magnification of the eyepiece.
A Barlow lens is nice for observations of targets which require more magnification as for example planets, but it also reduces the image quality slightly. There are entry level Barlow lenses (with 2x, 2.5x, 3x magntification) from Baader or Celestron and more high quality products like the TeleVue Powermate series.
For solar filters you have to be very careful, especially with children. Always make sure that it is secure to look through the eyepiece and that the filter won't move. You can either see the sun through a foil filter similiar to eclipse goggles (like this: Baader Solar filter tube: 100-140 mm) or at specific emission line wavelengths like H-alpha. This however is really expensive for such large apertures that I would not recommend it with beginner telescope.