+1 on staying inside as much as practical.
That said, we all make decisions based on the perceived threat level. If you think the dogs are barking because of activity on the far side of the fence and presume that activity has not yet migrated across the fence-line, then sitting on the back porch isn't unreasonable.
My advice would be to invest in a good SureFire tactical light or a small bright flashlight to keep ready in the home. In these situations you can pretty well light up most back yards to identify your suspect. A cordless phone with a headset is a big plus since it keeps your hands free.
And there's nothing wrong with turning on the back yard lights
before you go outside.
I know that officers can't go on a person's property without a reason, what if they are pursuing a BG who committed a serious crime, and the criminal runs into residential property? Would the police be able to then tresspass in order to stop this dangerous person?
As previously said --
you betcha! Anyplace they see the bad guy go, they can go too. That means if the bad guy runs into your house the cops can follow (whether that's really a good idea or not is another thing). If the cops have a "reasonable belief" that the BG may have gone from a neighbor's yard into yours, expect --at the very least -- flashlights over the fence if not an officer entering your yard to investigate. Special note from experience: Be alert for plainclothes officers in these situations! Sometimes they are pressed into service during a pursuit and forget they're not in uniform.
Re: Command Voice
The use of a command voice (i.e. "Let me see your hands! Do it now!") often works, regardless of your LEO status or not. Back in the 70's we learned that assuming the role of authority often worked and many people/sheeple responded accordingly. In a situation where you can't see the person behind the voice a response of "Who are you?" is a first step. It allows the voice to identify themselves and to be aware that you can't see their uniform or "badge of office". If the response is "Police" or "Police officer" the wise move is to comply carefully but to ask "How do I know that?" Police officers will generally issue further orders to secure their safety and then identify themselves in due course. A BG who is "faking it" will probably get flustered and give themselves away.
Remember that security guards are "normal citizens" with no police powers. If they give orders, you can calmly and without offering any threat, walk away from them (into the house of course). Of course if the voice is very nervous and sounds like Barney Fife going through puberty, it'd be a good idea to say "I'm going inside to call the cops" first.
A perfect score on the Practical Police Course is 600. My brother, who's a life-long LEO shot a 560 that day, and I managed a 480. Some of the security guards struggled to get above 100.
Sadly, depending on the company, some security guards have trouble tying their shoes. I did security work to help put me through college when armed guards weren't rare. Out of 66 armed guards, the lowest PPC score allowed was 420 otherwise you didn't carry. Eight of us competed for top shooter and the scores ranged from 588-596 and twice I lost with a score of 594 based on the number of "X's".