Good questions, overall. It's nice to have some clarity for these things. Bear in mind that where possible, I am using the strictest definitions provided by Fifth Edition rules, and no other resources from previous editions. That's not to say that previous editions aren't necessarily used, but I'll make a note of it. Additionally, it is possible that these answers might vary from table to table. Also, I'm proud that I've beaten Xenon to the quotation wall of text this time.

1- i have trodes. do i need anything else for image link? soundlink?
Your trodes provide a direct neural interface (DNI), which transmits data like sounds and images directly to your brain.
A direct neural interface, or DNI, connects your brain to electronic devices. Direct neural interface (along with a sim module) is required for VR use, but DNI is also useful for AR in that you don’t need any additional gear like earbuds or an image link to see or hear augmented reality objects.
How do you sign up? You get DNI by wearing trodes, or having an implanted datajack, commlink, or cyberdeck. And if you’re using a sim module along with your DNI, you can get a sort of “super AR mode” where you can also feel, smell, and taste your AR experience.
2- i have cyber-eyes. do i need anything else for image link?
Cyber eyes come with a built-in image link.
Cybereyes: The basic cybereyes system features 20/20 vision for both eyes, an image link, and a built-in camera at no extra cost, as well as capacity for vision enhancements.
3- i have a datalink. do i need anything else for image link? sound link?
By datalink, I suppose you're referring to a datajack. Datajacks are used to provide direct neural interface (DNI). DNI provides you with the same benefits as image link and sound link.
4- i have no cyberware, but i DO have a smartgun, and goggles with the smartgun feature. what bonuses do i get?
You get the +2 to Accuracy, and you get +1 to your dice pool to shoot the weapon if your smartgun is wirelessly active. Bear in mind that you need a way to connect the gun to the goggles, which can be achieved via wired connection for security, or wirelessly for ease of use and the bonus to your dice pool.
If you’re using a smartlink, the smartgun system increases the gun’s Accuracy by 2. The smartgun features are accessed either by universal access port cable to an imaging device (like glasses, goggles, or a datajack for someone with cybereyes) or by a wireless connection working in concert with direct neural interface.
...
Wireless: A wireless smartlink provides a dice pool bonus to all attacks with the weapon: +1 if you’re using gear with a smartlink or +2 if you’re using an augmentation for which you paid Essence. Ejecting a clip and changing fire modes are Free Actions.
5- same as 4, but i also have trodes.
The line in the smartgun blurb about working with wireless and a direct neural interface seems confusing. But bear in mind that your trode net has a univseral data port (UDP) like all devices. Therefore, you can just run a wire from the gun to your trodes and establish your DNI that way. However, you still only get the bonus to your dice pool if your smartgun is wirelessly active. All using the trodes do is circumvent the need for goggles or other visual aids.
6- i have a control rig. do i need anything else for image link? sound link?
Your control rig provides DNI and also is essentially a datajack.
Control rig: This implant harnesses the raw data-coordinating and synchronization power of the middle brain for the express purpose of directly manipulating rigged vehicles and drones (and other devices with rigger interface, like turrets). It has a built-in sim module, so you can use it for DNI with other devices. It also comes with a universal data connector and about a meter of retractable cable (it’s like getting a free datajack).
7- i have cyber-ears. do i need anything else for sound link?
No. Cybernetic ears come with a built-in sound link system.
Cyberears: Ordinarily, cyberears replace only the inner ear, although the whole thing can be replaced as well if you like. Cyberears offer hearing with normal ranges (like an omni-directional microphone), a sound link, and Capacity for modifications and enhancements.
8- what is the complete list of ways to get a DNI?
Trodes, datajack, implanted commlink, implanted cyberdeck, control rig (this isn't listed in the following quote, but the equipment description says that it provides DNI).
How do you sign up? You get DNI by wearing trodes, or having an implanted datajack, commlink, or cyberdeck. And if you’re using a sim module along with your DNI, you can get a sort of “super AR mode” where you can also feel, smell, and taste your AR experience.
9- can i install image link in my meat eyes without replacing them? sound link in ears?
Yes. Any item listed as an Augmentation can be implanted by itself unless otherwise specified.
One final note about cyberware (this doesn't apply to bioware). All cyberware has a neural interface. This is
not a DNI. The neural interface allows the cybernetics to be activated and deactivated without needing wireless connectivity. However, if you have cyberware that gets a wireless bonus, this bonus
only applies if the cyberware is wirelessly active.
Besides their wireless functionality, almost all cyberware devices are equipped with a neural interface (not to be confused with DNI) that lets you mentally activate and control their functions. You can use this in place of wireless control, preventing wireless hacking, as long as all of the “moving parts” are connected to your nervous system. An item that has a wireless bonus, however, can
only gain that full level of functionality if wireless functionality is active.