Are levayah attendees obligated to say Kriyas Shema?

The people who are needed to carry a coffin to burial are exempt from Kriyas Shema. The rest of the funeral party is obligated. They should pause momentarily to say the first pasuk; the rest can be said while they are walking. In order to avoid a conflict between the mitzvos of Shema and escorting the deceased, the funeral should only be scheduled after the Chevra Kadisha and most of the public have already davened. Once the sun has set, the funeral should only begin after most people have davened Ma'ariv. 

סעיף א-ב ס"ק ב,ג,ד,ו

Can a burial be pushed off until after sunset?

There is a Torah prohibition against delaying a burial overnight. The poskim disagree about whether it is forbidden to delay the burial into the night or whether it is only forbidden to delay the burial until the next morning. If delaying the burial is necessary for the honor or needs of the deceased, doing so is permitted. There is also a positive commandment to make sure that the burial is done before sunset. Therefore, a burial should not be delayed until after Ma’ariv if it is possible to do it before sunset.

ס"ק ו; ביאורים ומוספים דרשו, 5

How long must one accompany a levayah?

One who joins a levayah performs a great chesed for the departed. As an extension of the mitzvah of gemilas chesed, one is obligated to join a levayah. The poskim disagree about whether one is only obligated to escort the deceased for a distance of four amos or whether one should continue all the way to the cemetery. Some people (who are not escorting all the way to the cemetery) opt to accompany the funeral for a short distance and then remain standing until the procession continues out of view.

ס"ק ג; ביאורים ומוספים דרשו, 2

• For the most part, an onen is obligated in mitzvos on Shabbos and Yom Tov. The poskim disagree about whether learning Torah is permitted. If an issue arises regarding the funeral or burial on Shabbos or Yom Tov, the onen is exempt during the time that he needs to take care of the matter.

• On the first day of Yom Tov, it is permissible to ask a non-Jew to bury the deceased. On the second day of Yom Tov, the burial may be done by Jews. Either way, the relatives are still in the category of onenim and are exempt from mitzvos.

• It is forbidden to daven, learn, or say a brocha within four amos of a dead body or grave. Doing mitzvos is a form of mockery to the deceased, who can no longer perform mitzvos. 

• What is the appropriate way to say Kriyas Shema?

• How can one protect his heart when reciting a davar shebekedusha?

• Do Birchos Kriyas Shema have to be repeated if they were said while one was improperly dressed?