It depends on the size of your dog. Most burglar alarm systems won't pick up a dog 40 pounds or less. If your dog is the size of a person, you're out of luck.
You can have a burglar alarm system, but motion detectors probably won't work for you. Alarms wired into all of your windows and doors will be more expensive than a motion detector, but they won't be set off by your pets.
If you have motion sensing equipment then any movement will set it off, whether it is an animal or person. If someone opens a door or window it will go off. If someone breaks a windo the alarm will also go off.
Yes. A wireless security system is just as effective as a hard wired security system. Wireless systems even have many advantages to hard wired systems. For example. wireless systems cost less to install because consumers don't have to pay for the labor of drilling and running wires in the walls all over the house. Also, wireless sensors can be placed anywhere (because you don't have to find a spot on a wall that you can drill in to and run wires), which can allow senseors to cover a greater amount of area in a home. Wireless security systems are cellularly monitorred (instead of the company monitoring your security though a land line). Most hard wired security systems now use cellular monitoring as a back up system. This is great because if something compromises the ingtegrity of the landline, the security system can still send out a signal. Wireless systems can also have a back up system using a static IP address through an internet connection, although most major security companies do not currently offer this feature because the damand is not yet great enough. Another advantage of a wireless security system is that you can take the equipment with you when you move to a new appartment or house.