I have several important questions regarding Hajj issues. I hope you will answer them at your earliest convenience.
1) What should a pilgrim do with his/her Ihram after performing Hajj (keep it (for example for shroud in which this person will be wrapped up after death) or deal with it like with any other cloth etc.), i.e. what is the etiquette of dealing with the used Ihram?
2) Is it permissible for a man to perform Hajj on behalf of a deceased woman and vice versa?
3) Is it permissible to perform Hajj on behalf of a deceased person who did not pray during life out of ignorance (did not know the correct Arabic prayers or was lazy to learn them but recognized the importance of Salah)?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The clothes of Ihram do not have any merit over other clothes. If one wants to make them one's shroud, there is no harm in doing so.

Imam Abu Dawood asked Imam Ahmad about a man who prepares his shroud and performs prayers in it or uses it as his Ihram and then he washes it and keeps it to be enshrouded in it. Imam Ahmad liked this idea. He said: “I prefer a new or clean shroud.” He disliked wearing a shroud to avoid soiling it.

There is no particular etiquette concerning the clothes of Ihram. If one wants to make his Ihram as his shroud, then he should not soil it by frequent use.

Performing Hajj on behalf of a deceased person is recommended provided that the person himself had performed his obligatory Hajj.

It is also permissible for either a man or a woman to perform Hajj on behalf of another man or woman.

As far as performing Hajj on behalf of a person who believed in the obligation of the prayers but neglected them due to laziness, the Muslim scholars differed in opinion on this issue due to their disagreement regarding such a person if he is a Kafir (non-Muslim) or not.

Anyway, you can perform Hajj on behalf of such a person based on the opinion of the majority of the Muslim scholars, who see that neglecting the prayer due to laziness does not constitute Kufr (disbelief). If you do not perform Hajj on behalf of such a person, it is also correct according to a group of Muslim scholars.

Allah knows best.