I would like first of all to thank you for your question which reflects your keenness to learn about Islam and explore it.
In your question, you have touched on a very important, yet very misunderstood topic that relates to the Hereafter; that is the topic of intercession.
Muslims believe that intercession is one of the great gifts that has been particularly given to the Prophet Muhammad (peace be upon him).
The Prophet referred to this when he said:
“I was given five things which were not given to anyone before me; I was given support by casting fear in the hearts of my enemies who are a month-travel distance away from me, booty was made lawful for me and it was not lawful to any before me, the whole earth has been made a place of worship for me so, when the time of prayer is on for anyone of my followers, he can pray wherever he is, and I was given intercession and every prophet was sent to his own people while I was sent to all human kind.” (Al-Bukhari)
This great gift that was specially given to Prophet Muhammad is something that aims to honor him first, and then give a chance to his followers (those who worship Allah from the depths of their hearts, yet sometimes fail to keep up the good work because of their human weaknesses) to be saved, and pardoned.
Intermediation vs. Intercession
As you mentioned, intermediation is not accepted in Islam when it aims at delivering things that is not your right to you or when it aims at violating the rights of people and taking what one does not deserve.
Yet, since Allah’s mercy covers and embraces everything, Almighty Allah delivers it to people.
He can do so directly, but as a way of honoring our beloved Prophet, Almighty Allah makes some of that mercy be delivered through his person.
To exemplify this, we can say if there is a class where the teacher wants to honor one of his students and raise his rank in front of the rest, he may say, “Because of you, I will forgive these students who did their best to do their homework but could not do it perfectly.”
Here the teacher is doing two things at the same time: He is honoring his excellent student and also showing his love and mercy to other students who tried to do their best.
This mercy is not for the lazy ones, but it is for those who tried but could not achieve it to the best.
Therefore, the whole thing is not loose or open for anyone.
Our Good Deeds Will Intercede For Us, Too
There are qualifications for a person who will enjoy the intercession of the Prophet.
Such qualifications are mentioned by the Prophet in his hadith that goes:
The happiest one who will deserve my intercession on the Day of Judgment is the one who says, ‘There is no God but Allah’ with sincerity of his heart. (Al-Bukhari)
The concept of intercession in the broader sense also covers the intercession of good deeds on behalf of a believer.
As much as our bodily organs will be a witness against or for the person on the Day of Judgment that he has committed certain deeds, our good deeds will come to intercede in his favor on that day.
In another hadith, we read:
Fasting and the Quran will intercede for a person on the Day of Judgment; fasting will say: ‘O Allah! I have prevented him from food and drink so allow me to intercede on his behalf.’ And the Quran will say, ‘O Allah! I have prevented him from sleeping at night (because he was busy reading), so allow me to intercede in his favor.” Almighty Allah will allow them to intercede.’ (Ahmad)
Therefore, we can grasp that it is not an issue of laziness that people are told about the Prophet’s intercession.
Rather, it activates them to work hard in order to deserve such an intercession, as it is only for qualified people.
It Increases Our Love for Prophet Muhammad
Moreover, granting the gift or the status of intercession to Prophet Muhammad (peace be upon him) links people to him and increases their love for him and shows how much he cares for hisUmmah (nation).
On the Day of Judgment when everyone is busy with his or her own destiny, Prophet Muhammad will be there standing up for the good of his nation and working for their benefit.
This definitely confirms the fact that he is a mercy to mankind and he is merciful to the believers. Almighty Allah says in the Quran:
Certainly a Messenger has come to you from among yourselves; grievous to him is your falling into distress, excessively solicitous respecting you; to the believers (he is) compassionate. (Quran 9:128)
Now, coming to the issue of the martyr and that he or she is given the ability to intercede for 70 of his or her people, this is mentioned in the hadith that goes:
…A martyr will be permitted to intercede in favor of seventy of his family. (Abu Dawud)
Some people may wonder why that is. The answer is quite easy and simple.
Martyrs are basically people who die in defense of their land, their families, their honor, or their possessions against any aggressor.
Such people who give their lives for others to live on, are great people who deserve to be honored on the Day of Judgment.
As much as they sacrificed their lives to save others in this world, they are given the opportunity to save their believing family from destruction in the Afterlife.
Definitely this covers those who are qualified as we mentioned earlier.
Again, this is a rank of honor in which these people are placed for what they have offered.
Yet this by no means excels or comes close to the rank of the intercession given to Prophet Muhammad, as this is specific, while the other is general, and surely there are big differences between both.