1. How can I check for collision between objects in the room. Say, I have 2 TVMesh Box1 and Box2. How can I check for collision between these two. I am using TV3D 6.5. Any tutorials available?
If you only need to do checks between simple shapes (spheres/elipsoids, boxes, cylinders) of the same type you can find various algorithm for all these shapes using google. If you need something simple like sphere-to-sphere or box-to-box without rotation, you just need to check for bounds and distances (for spheres).
Only efficient way to do collision detection between two arbitrary meshes, according to my knowledge, is to use TVPhysics.TestCollision(...). For this you need to create two mesh bodies or one mesh body and one static mesh body. S=You can't use two static bodies. Mesh bodies are all right but they can only be represented by convex hulls. So depends what you need.
Alternatively you can get the face data and implement collision detection of your own. AABB, BSP and Octree would be things you might want to have look at.
Is there an algorithm to check if a polygon is simple/complex.
In TV3D - No.
In general - what do you mean by complex polygon?
Concave? If so, they yes. You just have to check if the polygon has any interior angles greater than 180deg. If all angles are smaller than 180deg, polygon is convex.