With these adapters the cat5 cable can power the camera?

These adaptors worked for me, and they did power the cameras, i like the idea of using CAT5 cable.

Can these be used to convert POE cameras to analog system

I think typically it's the other way around. Ethernet cable is so much easier to route through walls. I don't know why anyone would want to switch from an ethernet cable system to a coaxial cable if this is what you consider analog. POE is power over ethernet. BNC cable is coax and power packed into one wire sheath with big honking ends that are hard to send through walls. Either can transmit digital or analog signal I believe so it's hard to understand your question. Both coax and ethernet transmit signal through unbelievably small wires inside the cables. So you can convert POE to BNC or BNC to POE.

can I used for outer door

I have used the product out door however, I recommend using a weather proof 2X4 box to house the balun or placing it in an area where it will not be exposed to weather conditions. I will gladly send you a photo of the box and setup that I have used for housing the balun outside.

I do not want to use the power . should connect the powr to work?

There are cheaper options if you want signal only. The camera needs power so just one of these can bring power then you can split the power to the cameras in the vicinity and you can use ones that don't carry power to the rest that only require signal now.