Simona Elena

To answer your last question first -- no, you cannot ever enter the US with a tourist visa planning to adjust status.  You can use the tourist visa to enter the US and marry, but then must leave and apply for the immigrant visa.  There is no visa that allows an LPR to bring a fiancee to the US to marry and adjust status -- only a US citizen can do that. 
 
In addition, it would be close to a year before you would get any document that would allow you to return to Romania to resolve custody issues for your son.  And somewhere along the way after you marry, you'd need to file a petition for him to get an immigrant visa to return with you to the US.
 
The plan that is likely the fastest is to marry in Romania, submit the I-130 for you (and your son, as a derivative on your petition), and complete the visa process for both of you once the petition is approved.  While that is going on, you can do whatever court process you need to for your child, so hopefully all that will be resolved when you receive this visa.

There are a lot of posts here on VJ about the difference in the requirements and what happens if an LPR naturalizes before the F2 is granted.  (Answer:  They have to file a new I-130 petition(s) for the child(ren), as the spouse will get an IR1 (or CR1), so there is no derivative v u sa available for the child.)  
 
As to why -- the simplest answer is because that's the way Congress wrote the law.  (The same differences occur in non-immigrant visa categories.  For example, H1 and L1 visas allow dervatives for spouses and children, but B1/B2s do not.)  There are a lot of factors that led to the difference in immigrant visas processing.  One of the primary ones -- that works to the benefit of the US citizen -- is that the issuance of an immigrant visa to a child (IR-2) relies only on the relationship between the child and the US citizen parent.  If, for example, the spouse does not qualify for an immigrant visa under one of the ineligibilities Section 212(a)  -- health, crimes, drugs, fraud, overstays, etc -- a visa can still be issued to the child.  If the LPR's spouse does not qualify, the children cannot be issued visas either, since their qualification is derived from the parent's qualifications .

Simona Elena, you can trust jan22 completely when it comes to visa types and protocol.  The conflicting information in this thread is incorrect.

If they marry and he petitions for them, only one I-130 petition would be required.  The F2a category allows derivative applicants, so he would file for the OP (once married, of course) and the child would be a derivative of her visa (as a child if his biological son, or a step-child if not).
 
The link is not relevent for this case...it is for adopted children, not step-children.

But it's in the adoption section of the USCS website (as shown at the beginning of the link:  uscis.gov/adoption/immigration-through-adoption...).  There is no need for the OP to think that the only way to immigrate with her son -- by being petitioned by her boyfriend-turned-husband -- is to meet all of the adoption-related criteria.

On your own there is no was for u to permanently immigrate
If your bf wants u to join him,  he should return and marry u , get all the required documents from u he would need for a spousal visa (F2a)  
He should join this site and ask how to do this and read the guides above 
he would need to file 2 petitions for u and son if the son is his
If not his  the following web page is for step children
 
https://www.uscis.gov/adoption/immigration-through-adoption/family-based-petition-process/immigration-adoption-and-citizenship-for-stepchildren-of-us-citizens-and-lprs