Does my utility room need fresh air? If so, possible solutions?

Question

Our home has a ~ 13' x 12' utility room that houses our HVAC system and gas hot water heater.

Adjacent to this room is another room that we would like to use for an office. Currently those two rooms are connected by a louvered door. The problem with this is that when the heat or AC is running the blower is too loud to be able to really use the adjacent room if e.g. one were to be on the phone. We need a way to replace this door with a solid door to minimize the sound without violating any building codes and/or putting ourselves at risk.

This is all fairly new (~ 2 years) construction, so the furnace (as far as I can tell / understand) is drawing in fresh air directly from outside (see pictures in link below). I'm less clear about what the venting requirements are for a gas hot water heater.

Pictures of the space

So, my questions are:

1. How would I go about determining if a source of fresh air is a requirement for this room?
2. Even without the louvered door it's not as if this room is air-tight. For example, you can see that the drywall does not go above the bottom of the rafters. What exactly qualifies as a "source of fresh air"?
3. There's a small window in this room. If we determine that we do need to provide fresh air to this room, could we utilize that window in some way, or is there a certain size requirement for the source (and if so, how would we figure out what that size requirement is)?

Edit #1:

As requested, additional photos of the top of the hot water heater:

Hot Water Heater

Edit #2:

OK, did a bit more reading, in particular about combustion air requirements (secondary source)

As I understand, the calculations then are as follows:

The input BTU/hr for the hot water heater is 38,000. The furnace is ignored since it is enclosed and draws directly from outside (is this correct?)

The room is 12' x 13' x 8', which amounts to 1248 ft^3. For 38000 BTU/hr a minimum of volume of 1900 ft^3 is required (38000 * 50 / 1000)

The required area for a vent is 1 in^2 / 1000 BTU/hr, so 38 in^2 (but I guess the minimum vent size is 100 in^2 - this part isn't clear to me)

So if we were to replace the door, we would need to install two, 100 in^2 vents, one within 12" of the ceiling and one within 12" of the floor? Is this correct?

Can the space between the top of the drywall and the floor (see the first set of pictures) serve as the top vent? The basement is a drop ceiling, otherwise that would be a free gap in to the room next door. I would think that combined area would make up for the fact that the drop ceiling adds resistance to air flow.

Answer 1

In the remodels I have done with open combustion inside a house we were required to have the 2 vents I normally put 1 in the wall close to the ceiling and one in the wall at the floor with each being ~1 sq ft vented to the attic on single story. This is for fresh air not exhaust and I was told having the 2 zones helps to mix the air in the room and the exhaust goes out the vent on the water heater. I thought it sounded excessive but was easy to bring the vent’s in a non load bearing stud chase both were on the same one and by cutting out most of the walls top plate between these 2 studs on a non load bearing wall provided enough to pass inspection. This passed inspection the handful of times I did it, one being on my own home when I converted it to gas. On 1 home I was required to install duct work in the stud bay and connect the vents , the vents must be fixed no dampers. The home that I was required to use ducting was a multi family dwelling and the wall I was using was common but not load bearing, the duct is easy to install remove the Sheetrock down 1 stud bay and purchase square duct put it in the bay replace the Sheetrock install the vents and it ends up looking like part of the heating system. If you can just use the stud bay cut the holes for the vent registers cut through the top plate I used a reciprocating saw so those were easy.