Welcome to Radio Reference! Unfortunately you are not going to be able to specifically monitor any of the departments you listed with the scanner you have, because as you said, it will not do trunk tracking. Monitoring the trunking frequencies conventionally, you will be able to hear all the traffic on this system, but you won't exactly know what agency is talking and if the system is busy, you will likely not be able to follow any conversations.
Since you are new to all this, here is a brief explanation of why you cannot do this: Conventional radio systems use one frequency per channel on their radios, so switching from channel 1 to 2, you would switch from one frequency to another. In reality, there are a fixed number of frequencies available, and in a county with a large population like the one you're in, the public safety frequencies get licensed(read now unavailable to anyone else there) pretty quick. If you look at all the talkgroups listed in the
Carrollton Public Safety TRS, if it were a conventional system, each one of those would require a separate frequency.
In trunking though, you can think of each talkgroup as a channel on a radio, so the FB PD and FD each have four or five channels assigned to them, but the way this works, is that all these different agencies share those 9 frequencies listed at the top of the database page. One of these frequencies is called the control channel, and it continuously transmits data to every radio on the system. What this data does is say if a Farmers Branch Police officer keys his radio up on "Channel A"(talkgroup 52272), before the officer can speak, the control channel sees the radio keying up, and assigns one of the other available frequencies to that talkgroup, so now every other radio on the system whose channel selector is set on this "Channel A" will now switch themselves over to this new assigned frequency so they can hear what is being said(everybody thats not on that channel hears nothing), and after the officer is done talking and releases his PTT button, all the radios switch back to listening to the control channel for the next instructions. All this frequency switching is done internally and goes pretty much unnoticed by the user; all they have to do is turn their radio on to the proper channel(talkgroup).
That's an overly simplistic explanation of what happens, and different types of trunking accomplish this in different ways. You can read up on trunking
here. There looks to be quite a bit of conventional public safety frequencies in Dallas County(though I'll let others from the area make suggestions) so you should be able to get some decent use out of the Uniden you have now, but just be warned. After getting a taste for public safety monitoring on conventional, and you know that your hometown agency is on a trunked system, it won't be long before you break down and buy a trunktracking scanner. At least that's what happened to me.