1: Yes
2: Yes, that is called the "accessory port". The speaker plug comes ut of the connector plugged into that, as well as the ignition lead, which is required to be connected to 12v + in order for the radio to power on. This is a standard part of the radio package.
3: eBay is full of cheap accessory connectors. If you need a programming cable as well as the speaker/ignition dongle, you can actually get these in one assembly. For programming you will need a RIB box as well.
Programming Rib Cable Motorola LP Spectra VHF UHF Astro | eBay
If you just want the speaker connector alone, see below.
Speaker Ignition Cable for Motorola Spectra New | eBay
4: Which screws do you want to remove? The Spectra case uses Torx (star) and Allen bolts. You can get a multi tip screwdriver with removable tips that fit these.
5: The front face/head is removed by removing the two Allen bolts on each side of the front of the face. The faceplate pulls off, and it is electrically connected to the body of the radio by a interface board, which can also be pulled off the unit by hand. Once removed, you can even separate the two using a used Spectra remote kit that can be found around $25-40 on eBay.
Paul