All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There are some conditions for a marriage contract to be valid, the most important of which are the consent of the guardian and the presence of two witnesses. Therefore, if the first marriage took place with the consent of your guardian and the presence of two witnesses, then it is a correct marriage contract. Not making the marriage public does not affect the validity of the marriage contract.
However, if the marriage took place without the presence or consent of your guardian, then the marriage contract is void according to the most preponderant opinion of the scholars .
An incorrectly conducted marriage contract must be invalidated unless a Muslim judge rules that such marriage is valid, in which case it is considered as valid.
Even if we consider that this marriage contract is void, this does not mean that the wife has the right to remarry with another man whenever she wishes, rather she is not permitted to do that until the marriage contract is invalidated or divorce takes place and her waiting period expires.
For more benefit on the conditions for the validity of the marriage contract, please refer to Fatwa 83629.
As regards the divorce paper which you mentioned, then writing the word divorce is one of the metaphors of divorce, and therefore divorce does not take place unless one intended it, or that writing the word divorce is accompanied by uttering it. If we assume that divorce took place, then it should be taken into account even if the marriage is void.
With regard to your husband saying to you that you are his wife after that, then if we assume that the first marriage contract was correct and that divorce took place, this statement means that he is taking you back if this divorce is revocable, because a husband may take back his wife if she is still in her waiting period, and the waiting period of a pregnant woman ends when she gives birth to the baby. For more benefit, please refer to Fatwa 83672.
Concerning what you stated as the second marriage, it is an invalid marriage in any case, because it either took place while you are still married or that it took place while you were still in your waiting period. Marrying a woman who is still a wife of someone else is void, and marrying her while she is still in her waiting period is also void. You are obliged to repent to Allaah for not confessing before the court registrar that you are pregnant.
As regards abortion, if it was a miscarriage without any involvement from both of you, then you are not sinful; however, if one of you caused it, then whoever caused it is obliged to repent. If this abortion took place after the sperm-drop became a clinging clot which does not melt if hot water was poured onto it, then a Diyyah (i.e. blood money -which is one-tenth of the Diyyah of the mother [if the abortion took place 120 days after the egg is conceived]). For more benefit, please refer to Fataawa 90279 and 85970.
To conclude, if the first marriage contract was correct according to the conditions which we mentioned for the validity of the marriage contract, then you are still a wife of the first husband and it is not permitted to anyone else to propose to get engaged to you, let alone to marry you. But if divorce took place and your waiting period expired, you are free to marry, so you should choose the best husband with regards to religion and good moral conduct. However if the marriage was incorrect due to the non-consent of the guardian and a Muslim judge or his deputy did not rule that it is correct, then you are obliged to ask for this marriage contract to be invalidated and it is not permissible for you to continue this marriage. However, since the marriage was not invalidated, it is not permissible for the second husband or anyone else to marry you.