You have to talk with your employer about the procedures/documents to apply for your baby's visa, especially if you are going to do it inside Thailand.
There are companies that don't (or cannot) support employees or family members if they are overstaying or illegally staying in Thailand for their own reasons.
Better be careful to think no problem for children to be overstaying, especially if the main applicant is a Non-B holder.
Technically, yes, it's within 72 hours before arrival, but the system is open for 4 days including "today" as a window for TDAC submission. (day counts at 0:00/ midnight ICT).
Basically, yes, you are expected to submit the first 90-day report after arriving in person at the local immigration office. In many cases, those "first reports after entering" online submissions are rejected, but it seems some offices accept online submissions. There is no harm in trying online first within the reporting window, which is between 15 days and 7 days before the due date. If rejected, you can visit the local office to submit in person within 7 days after the due date.
, If you have already used a 60-day family visit extension with the current series of visa and extensions, you cannot apply for it again. 60-day family visit extension is a one-time deal per visa.
No, unfortunately, Savannakhet or any other place no longer accepts in-person applications. All Thai embassies and consulates are now on the eVisa system. You go to one of the neighbouring countries, apply for a visa on the eVisa website using an entry stamp for that country, wait for your visa to be issued, then return to Thailand.