Electrical system Camper van battery charging

Hello,
I am from the Netherlands and can read replies in Dutch as well.
In my camper van, I have the following electrical installation :

Battery (10 years old): Super-B : SB12V160E-ZC (2016), including integrated BMS
Battery Monitor : Victron : BMV-700
AC/DC converter : Victron : Multiplus Compact 12V 1600 VA 70 Amp
DC/DC converter for Euro 5 engines : Top Systems TS 800

I only have basic understanding of this electrical system.
I am now trying to figure out its principle mode of operation and if the below basic statements are correct :

  1. When the car engine is running, its alternator will supply a (variable) DC voltage
    to the Top Systems DC/DC converter.
    This converter then produces a constant DC voltage to the BMS of the battery.

  2. With the car engine is not running, I can also hook up a 240V 50Hz external power supply which “feeds” the Victron AC/DC converter.
    This converter then produces a constant DC voltage to the BMS of the battery.

  3. The BMS of the battery then ensures the battery is charged properly according its SoC
    level (bulk/float/absorption/and/or any other relevant parameter).

I would highly appreciate a reply confirming above basic and simple statements
are correct.