Is it permissible for a Muslim to escort his deceased disbelieving relative to his final resting place?

It is permissible provided that he doesn`t walk behind non-Islamic symbols, rather he should walk in front of them.

Is it permissible for the man to go out wearing shorts?

It is permissible as long as his Awrah(private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed.

I work for a company whose manager refuses to allow employees to leave during work hours. Do I incur sin if I secretly went out to join the congregation at the Masjid? Is doing so considered a breach of trust?

Praise be to the Lord of the Worlds.

We recommend that you pray at work to encourage your colleagues to follow suit, because whoever guides to good has the like of the reward of the person who actually does it. And Allah The Almighty Knows Best.

Should water be put in the deceased`s mouth and nose while washing him/her?

No, it shouldn`t.