1. If I am not mistaken, it is a beacon although granted, it's unclear what defines a beacon, Garrus calls the thing on Mars a beacon as well in this scene. But regardless, we don't really know what the beacons can or cannot store.
2. Kai Leng actuallyy copies Vendetta into his omni tool and carries it out of the building. 
Interesting catch about the terminology Garrus used. Maybe there was a beacon in addition to the other artifacts on Mars? Or maybe, whoever wrote the dialogue just wanted to somehow simplify the terminology.
That the depository on Mars was referred to as an Archive infers multiple items / information sources. I guess there were 3 intact ships, a supply of refined eezo, and perhaps other goodies left there as well.
Well based on Vigil and Javik's speech beacons were used as communication tools. Able to send and receive messages right to the person's mind. It has probably become a catch all term for them. But I would but Mars Archive and Thessia closer to data bases or maybe servers.
But can't copy the rest of the information in the tower. Did kind of forget about that.
Yeah, the beacons were supposedly capable of transmitting (and apparently storing) messages and data. The "artifact" on Thessia is referred to as a beacon by multiple people, including Javik. It also looks rather like the beacons we saw on Eden Prime and Virmire.
The artifact in the central repository on Mars looks a bit different, though - rather like some configuration of very large Prothean Echo Shards, which I guess makes sense as they are data storage devices.
Either way, there seem to be some inconsistencies in the way the various technologies were handled in the story. There is an implication that beacons are designed to transmit information directly into a Prothean mind (including someone with the cipher), yet Vendetta appears to pop out of the Thessia "beacon".
The artifact on Mars is directly accessible through terminals, and apparently its contents can be downloaded and erased from the source, which is what Eva Core was doing.
The inconsistencies make it a bit difficult to discuss any of the fine points around these technologies.