Yes you can used Tiled maps. Though not natively supported, a few of us have designed importers.
Here's mine that I've started working on again:
http://forum.thegamecreators.com/?m=forum_view&t=210176&b=41
Clonkex has built upon my older version and added additional features such as support for objects and properties.
http://forum.thegamecreators.com/?m=forum_view&t=209341&b=41
While I believe AppGameKit does have some level of garbage collection, you would still want to delete images and free arrays when you know you won't be using them again.
I'm not familiar with those games, but looking at a youtube video of incredible jack, that should entirely be possible in AGK.