Second Sprinter alternator capabilities while driving?

[FarmHand357]

Hello; long-time lurker here. I searched for a number of these terms unsuccessfully so apologies if this is a duplicate:

New build in process from SMB North. The second Sprinter alternator is listed as capable of 270 amps or up to 3400 watts. With 300 amp hours of LiFePO4 house batteries, does this mean they could be fully recharged from 80% discharge in about an hour?

With the optional 2.8KW inverter, does this mean that I could also easily run the back A/C as well as fully charge them during a roughly two-hour highway drive?

Are the up to 300 watts of solar on the roof additive to further reduce charge times during a bright, mid-day sun?

Thanks in advance!