How many panels can I have for this setup?
The number of panels is principally determined by the capabilities of your SCC. From what I can make out from your image, you have an Epever Tracer model #8415AN, which has a max PV input rating of 2,000W delivered into a 24V battery system, so the max number E20-327 panels you can connect is 6 (
6 x 327W = 1,962W is OK, but 7 x 327W = 2,289W BUST!).
Because your max PV voltage is 138V (at 25℃), you can only connect up to 2 panels in series (
2 x 64.9V = 129.8V is OK, but 3 x 64.9V = 194.7V BUST!) so the only configuration option you have is 2S3P.
As many as you like, or rather, as many as you need for your off-grid autonomy requirements.
Is the 100amp battery fuse sufficient?
Two aspects of solar system design determine the fuse protection requirements: (1) The anticipated load current +25% and (2) The rating of the cable.
Your anticipated load current will be 104A at 24V (2000W / 24V +25% = 104A) so fusing below this runs the risk of nuisance blowing. 4AWG cable is rated for 120A so fusing this cable would demand a fuse nothing higher than 120A, 2AWG is rated for 170A, so nothing higher than a 170A fuse, 0AWG 200A etc.
I would recommend using 0AWG cable to reduce resistive losses now and future-proof the design for a higher rated inverter (200A x 24V = 4,800W) and fusing the line now at 125A.
Goal: Run 3 window AC units (5 amp 450 Watts) plus laptop and monitors.
Whilst operating, your inverter is rated properly but AC units have a very large surge demand, maybe 2 or even 3 times the run-rate. You need to be sure that your inverter can cope with this.
Note: surge current will not blow an automotive-style fuse.
If I can run these ACs from 9am to 8pm weekdays
That is a huge demand!
450W x 3 units x 11 hours per day = 14,850Wh energy consumption per day, plus your other loads. 4 x 139AH at 12V is only 6,672Wh of battery and, because you shouldn't regularly discharge a lead-acid below 50% DoD, this is in effect only 3,336Wh. You'd only be able power this load for a couple, maybe three hours.
The Tesla packs come in 5kWh modules and around $1,000 each (used) you would need at least three to support that level of consumption.
Furthermore, your 1,308W (4 x 327W) array would only generate 6,540Wh on a good summer's day (
1,308W x 5 hours good sun = 6,540Wh) , quite insufficient to replenish your expected consumption.
You would have to expand your current design to just run one of these AC units.