Does general forgiveness from the family for theft absolve one of guilt without specifying the amount? Is prayer accepted with the intention of repaying the stolen amount in installments? Is it permissible to ask others to pray for one, fearing that one's own prayers may not be answered?

One's responsibility for stolen goods is not absolved merely by generally asking for forgiveness. Rather, it is absolved by returning the rights (stolen items or their value) or by seeking absolution after clarifying the right in detail. If you cannot inform them, then return the money by any means that does not cause harm or embarrassment. The fundamental principle is to return the full right immediately. However, if you are unable to do so, then return it according to your capability. If you repent and resolve to return the right whenever you are able, then your repentance and supplication are accepted, by God's will.