Despite you having a new relationship does not absolve your ex-husband from obligation of providing financial support to your children; however, for your eldest son, your ex-husband is not obligated by law to provide for him as he is at the age of majority (18 years old).
For your second query, the child will be considered under your first marriage.
These are some legal repercussion that may happen to you:
If you use the biological father’s surname, this can be used as evidence by your ex-husband in filing a case of adultery against you and the biological father.
If you inform the Local Civil Registrar that you are physically separated from your ex-husband, the LCR will not allow you to register the child under the biological father’s surname because of Articles 164 and 167 of the Family Code.
You can claim that you are single and then either leave the entry for the name of the father blank or use the biological father’s name; in this situation, you can potentially be charged with perjury.
If you use your ex-husband’s surname for the child, your ex-husband can file a case of damages against you.