Select the object and then click on the "UI" button two buttons to the right of the "Play" button. In the the User Interface that opens, set the density of the object to something low like 0.0001 and the object will be much lighter.

Thank you, this helps!

It's hard to say without seeing your model, could you upload it?

But here are some known issues:

exploding/recreating a group will sever the connection connections will only work on external groups you can only connect one object to controlled joints(motor, servo, piston,..) joints can only be one grouping layer deep

It would probably be better if you make an example model and post it, otherwise it's hard to grasp or even explain.

But here are some pointers:

if you want movable joints add them to a movable group(create a box, then create a hinge, now group them together) if you want those joints stuck to a static object simply create a new box, make it static, then connect the movable joint to the static box