What if a person who had been missing namaz (prayer) for years (like some of us do), and eventually start praying everyday. What he/she wants to overcome the missed prayers of all the years he/she had missed. How can one ask for forgiveness, how do one know how he is forgiven. The biggest question is, how do we know how our prayers are being accepted?
Also, is it possible to read qaza, if so till what time? Some people make it a habit, is it permissible to make fajar namaz, qaza?
A person may be born in a muslim family, but there comes a time when he matures and accept Islam as his religion at a conscious level. This is the time when a person truly "accepts Islam". This is the time when he realize that he has done a great sin by leaving all the prayers when he was a "muslim", and now he has to make up for years of prayers.
The companions of Prophet Muhammad (PBUH) found themselves in similar dilemma. They have a life-time of bad deeds that they have been doing before accepting Islam. Now that they realize their mistakes, they asked Prophet Muhammad (PBUH) what will happen to all the bad deeds that they did? Also what will happen to the good deeds that they did before accepting Islam?
Allah's apostle gave a beautiful answer (Sahih Muslim Book 1, Number 0217)
It is narrated on the authority of Abdullah b. Mas'ud that some people said to the Messenger of Allah (may peace be upon him): Messenger of Allah, would we be held responsible for our deeds committed in the state of ignorance (before embracing Islam)? Upon his he (the Holy Prophet) remarked: He who amongst you performed good deeds in Islam , He would not be held responsible for them (misdeeds which he committed in ignorance) and he who committed evil (even after embracing Islam) would be held responsible or his misdeeds that he committed in the state of ignorance as well as in that of Islam.
If you think that this situation applies to you, then you can be hopeful that your previous prayers have been forgiven, if you ensure that you do not intentionally leave any prayer from now on. Otherwise, you may be held responsible for ALL your left prayers.
It is also good to keep asking for forgiveness of your lost prayers.
In response to your main question I have to mention that every prayer has its frame which comes in the books. We are said that we have to watch our salat to be done as the orders. And hope and request Allah to accept that. As you know all of us have problems in our salat, but believe in grace and mercifulness of Allah to accept our incomplete salat.
For reading Qaza:
It is better to pay attention to this point that the salat is a right to God. It is not optional. when we accept monotheism and prophecy by tongue, we must prove it by act. That act is salat and fasting therefore when we have qaza in salat we have to offer them whenever we can.
I was trying to find a way to make up for missed prayers and I believe Allah has provided us an opportunity to be able to make up for all those missed prayers. My solution was to pray qaza for one day's prayers on Laylat-al Qadr. I have explained my process from thinking and planning to action, all here: https://islam.stackexchange.com/a/48732/28152 (Edit: actually here: https://www.facebook.com/notes/murat-kurt/ramadan-2018-looking-back-and-future/10156467646199532/)
