You would think they would only need to communicate silently through internal transmissions. Having them have to communicate verbally seems pointless. What is the IN-UNIVERSE reason for this?
Basic is (probably) a fall-back level of communication used when coordination of more sophisticated means isn't practical. In the case of battle droids, it may easily be sufficient, so more sophisticated methods simply aren't used t all.
We know that other methods are used with other droids, but that translation between them can be something of a problem. The primary function of C3PO (and presumably, other similar) droids is to act as a translator between communication protocols used by various other droids (and people). When Luke's uncle buys C3PO, his primary intent is to have him communicate with other droids (vaporators?)
At the level of individual soldiers, communication in battle is often fairly minimal (e.g., in our real life, much is often handled via simple hand signals). As such, it's probably more important to have some minimal level of communication assured, than to have a more efficient method that may not work at all at times (C3PO not necessarily being at its best under battle conditions).
In-universe, the most likely reason for programming the battle droids to speak in Basic is communication with non-droid personnel.
In several scenes, we see battle droids interacting with non-droids - usually their Nemoidian masters & operators. Here's an example from Episode I, but there are plenty throughout the prequel trilogy movies:
The droid invasion force moves out of the swamp and onto a grassy plain. OOM-9, in his tank, looks out over the vast ARMY marching across the rolling hills. A small hologram of RUNE and NUTE stands on the tank.
OOM-9: Yes, Viceroy?
RUNE: Captain, we've searched the ship and there is no trace of the Jedi. They may have got on onto one of your landing craft.
OOM-9: If they are down here, sir, we'll find them.
NUTE: Use caution. These Jedi are not to be underestimated.
While it would seem to make sense for droids to communicate with each other via some sort of binary language or wireless communication, it's possible that the Trade Federation simply cut costs by giving them a single, verbal communication method. Since they needed to communicate in Basic anyway, perhaps that was deemed enough and warranted no further research/spending.
1) They issued instructions to their enemies (I think it was 'drop your weapons' but could easily be wrong there).
2) The main thing they say is "roger roger", which seems sensible. In sci-fi or not, people assume that technology isn't working, unless it gives an acknowledgement. Particularly important if you are unsure if your damaged droids 'hearing' has been damaged. Go to UX.StackExchange and ask "I'm designing killer robots, how should they acknowledge orders by humans", they will say you should go with "roger roger".