Here is a website that had some information on the unit: http://www.acadiansingray.com/1st%20Batt.htm

To your questions, I will provide what I have found as it relates to the unit. According to Mr Bergeron's book, Guide to Confederate Units, the Cannoneers were stationed near Tyler, Texas at the time of the surrender of the Trans-Mississippi Department in May of 1865. The Federal government set up a number of sites for soldiers of the Confederacy to obtain their paroles. If you have a listing of members that were around at the end, their records might show where they got their paroles. From the web site note above, some of the members got their paroles at Alexandria or Washington, Louisiana, the paroles being given at the first of June. It is not shown if these people were in Texas at the surrender.

Money - unknown
Getting Home - If there were in Texas in May, and some in Louisiana in June, perhaps they were given transportion, via the railroad.
Sick Soldiers - I would suspect that the sick were sent to local Federal Hospitals till they were able to go home. I would guess they then got some sort of transportation, like the railroad.

Hope this helps. Other that the location of the unit at the surrender, everything is an educated guess.

JIMT