Praise be to Allaah.
First of all, we are happy to congratulate you on the great blessing that Allah has bestowed upon you, which is the blessing of Islam. Perhaps you felt the greatness of this blessing because of what you have seen in the changes in your situation and your feeling content, happy and peaceful. All of that is what Allah gives to those who utter the Shahaadatayn (twin declaration of faith) and that blessing increases as you act upon the rulings of Islam. We ask Allah to make you steadfast in adhering to His religion and to complete His blessings upon you both outwardly and inwardly.
You should note two important issues that have to do with prayer:
There is no excuse for the Muslim not to pray, no matter what his circumstances. In the case of a woman, she stops praying at the time of menstruation and nifaas (postpartum bleeding), but apart from that there is no excuse for anyone not to pray. The fighter on the battlefield prays, the one who is in prison prays, the one who is sick prays; that is because of the great importance of this obligatory duty according to the laws of Allah.
In the event of extreme or unusual difficulty in performing some religious duties, then Allah make it easier for him (by granting concessions). Because Islam enjoins the Muslim to pray no matter what the circumstances, there may be some concessions with regard to the rulings. So he should do whatever he can, and whatever he cannot do or is too difficult for him to do, is waived in his case.
In your situation, as you have described it to us, we say to you:
You should note that the basic principle concerning prayer is that it should be offered in a state of purity, covering the body, facing the qiblah and doing all the essential parts (pillars) and obligatory parts, adhering to the times prescribed in shareeah. Part of the easy nature of this religion is that it pays attention to the circumstances and situations of people who are praying, and it does not enjoin the Muslim to do what he is unable to do or what is too difficult for him to do. There may be a sick person in his bed, or a fighter on the battlefield, or a prisoner who is tied up, or one who is afraid to practice his Islam openly and pray openly - as in your case. In all these cases and similar cases, people are not required to do anything except that which is within their capability, and whatever they cannot do is waived. At the same time it is confirmed that their prayer is valid and they do not have to repeat it at all.
In many of our answers we have stated that which is appropriate to your situation of rulings having to do with your prayer, such as the following:
1. It is permissible for you to do the essential parts and obligatory parts of the prayer whilst sitting or lying down, making gestures to indicate bowing and prostrating.
2. It is permissible for you to put two prayers together if it is not possible for you to offer each prayer at its own time, or if there is sufficient time for you to offer two prayers together when you are in the best state with regard to purity, clothing and being able to do the essential parts and obligatory parts. So you could put Zuhr and Asr together at the time of either of them, and put Maghrib and Isha' together at the time of either of them. This is a concession granted by shareeah to everyone who is in a situation such as yours. In fact, if you are unable even to do this and you cannot offer each prayer at the right time even if you are sitting or lying down, or by gesturing, and you are not able to put two prayers together in the manner described, then you should offer whatever you can at the proper time, and for the prayers that you miss, you can offer them at whatever time is easy for you, when you are away from where your family can see you.
3. If you cannot do wudoo' or ghusl, then tayammum is acceptable in your case as an alternative to them.
For more information on the issues mentioned above, see the answer to question no. 100627
4. It is permissible to you to interrupt the prayer if you are afraid that any of your family members will see you praying.
See the answer to question no. 65682.
5. It is permissible for you to pray in a clean bathroom if you cannot find any other place in which to pray.
See the answer to question no. 153572
6. Until you can learn Arabic and memorise Soorat al-Faatihah, you can say instead of al-Faatihah, Subhaan Allah wa'l-hamdu Lillah wa laa ilaaha ill-Allah wa Allahu akbar (Glory be to Allah, and praise be to Allah, and there is no God but Allah, and Allah is Most Great), and continue to avail yourself of this concession until you are able to memorise this soorah. Perhaps you know that reciting it in the prayer is one of the essential parts or pillars of the prayer, so make it the first thing that you learn in Arabic and that you memorise of the Qur'aan.
See also the answer to question no. 3471.
7. The supplication (duaa') when bowing and prostrating does not have to be in Arabic, unlike the phrases that are prescribed in the prayer. So you can offer supplication in your own language regarding matters of this world and the Hereafter.
See the answer to question no. 20953
8. The same may be said concerning your clothing and hijab during prayer. If you can pray fully covered - everything except the face and hands - then do that. If the time for prayer is too short and you cannot put on the Hijab, then pray in whatever clothes you are wearing.
To sum up, you should do whatever you are able to do of the requirements of prayer, and whatever you are not able to do is waived in your case. Do not worry about whether the prayer is invalid or having to repeat it, because the prayer is valid and there is no need to repeat it. This is an example of the easy-going nature of Islam. And you can continue availing yourself of the concessions granted in shareeah until Allah make things easy for you and you are able to follow the rulings on prayer in full, and we hope that will be soon.
But we advise you not to hasten to disclose your Islam or pray openly if you fear that your family may cause you trouble and that you will not be able to bear their annoyance and harm.
We ask Allah to bless your family with guidance and to make things easy for you, and to decree for you a full and abundant reward for your struggle and patience, and to grant you a way out from the situation you are in.
We hope that you will not hesitate to correspond with us and we will give your questions a special importance in light of your situation. May Allah help you and take care of you.
And Allah knows best.