First thing to say, I am in the UK and have had a 120Ahr i3 for nearly a year. Things in the US are different!
Second thing to say, I suggest you join speakev.com. There is an i3 forum and there are some extremely knowledgable electrical engineers on that forum.
So, the i3 has a built-in 11kW charger. On ac at a public charging station (up to 22 kW, three phase) you cannot get more than 11kW due to the car limitation. On a UK three phase system, 11kW is around 30 amps. BUT if the supply does not have a tethered cable and you use your own cable as supplied or purchased this is more than likely single phase so you will get much less charging current. Rapid (dc) is the only fast way to charge your i3 on public chargers as you will get nearly 40kW.
Turning to your home wall mounted charger. As nearly every home user has only a single phase supply, nearly all wall mounted chargers are 7kW 30 amps which will charge your i3 in 6-7 hours if the battery is completely flat. The charger usually has a tethered cable which is rated for single phase 30 amps.
It sounds like you have a 3 phase supply into your apartment block but, apparently, only have a 16 amp wall box. Since you will almost certainly have a single phase cable then you will only get 3.5kW charging.
I cannot suggest how to proceed because I don’t know whether your wall box can deliver three phase. If it can and you buy a 3 phase cable (around £230 from BMW I think) then you will get a three phase power of root3 x 230 volts x 16 amps = 6.2 kW.
Hope this helps.