How can a non registered immigrant join the military?

No, sorry. Need to at least be a Lawful US Permanent Resident on a green card to be eligible to enlist.

Can organisation chart be amended to show associates reporting 2 different manager if L1A of their current mgr is rejected?

I agree. This is not the type of question to ask volunteer lawyers on a general blog.

I have opened asylum case, currently pending. In my country of origin they just enter martial law (Ukraine).

I agree. The enactment of martial law does not meet the asylum office's expedite criteria. Not even close.

Easiest is to have the employer's attorney request a duplicate approval notice for you.

Eb1-A visa for a virtual assistant?

You seem to be confused. Kindly analyze the requirements for the EB-1A category.

Need I a new F1 Visa?

Yes, you definitely need both a new I-20 acceptance issued by the new school, as well as visa issued in that new school's name.

What do I need to do if PennDOT office can't recognise my EAD?

Do as you have been instructed. That is your only hope at this point.

H1B - Change employer after I140 approval from Inida?

You need to consult with an experienced attorney via Skype to have your case thoroughly analyzed and receive the type of legal advice you are seeking.

Do you have to remain the US on an L2 during the EAD application process?

To qualify for the L-2 EAD, you need to have been admitted into the USA in L2 status. WT will not cut it.

Simply wait for 181 days and send in another I-765.