A google search brought up the following for William K. Bryant, which is a download. Depending on your browser, you may find it in your download folder. He appears to have had a fertile imagination.
(you will need to copy and paste this link)
You could check out the various regimental pages in the FIBIS Fibiwiki http://wiki.fibis.org/index.php?title=Main_Page
, with Search at the top of the page, to confirm the regiments were actually in India at the time, and whether there is any mention they took part in the Indian Mutiny.
As an example, the first man on your list is James BIRMINGHAM - 7th Regt. If you look at the Fibiwiki page 7th Regiment of Foot, http://wiki.fibis.org/index.php/7th_Regiment_of_Foot
, the link http://2day.uk/siteFiles/files/RRFLondo ... 660151.pdf
The Indian Mutiny broke out at Meerut on May 10th, 1857, and as soon as the news reached England, reinforcements including the 1st Battalion The Royal Fusiliers, were hurried out. This was the first appearance of the Regiment in India, but by the time it had arrived the worst of the rebellion was over. The final stage of the war was fought in central India, and after fighting of intense savagery, the rebellion was finally crushed at the end of 1859. The Fusiliers saw little of this action however, having been sent to occupy the Punjab, where it was imperative that British troops should be maintained to ensure that the population remained passive.
Findmypast (pay site) may have online records of service, in its Military category. However, if the men involved were discharged in India and came directly to Australia, many of the records have not have survived.
The muster rolls at the National Archives Kew would tell you where the men concerned were at the time of the Indian Mutiny (not available online). Perhaps an indication could be had from the online records on findmypast called “1861 Worldwide Army Index”
The East India Company Army regiments.
You could check out the various regimental pages in the FIBIS Fibiwiki.
James BRUCE - Madras Artillery
The Madras Artillery, at least some of it, took part in the Indian Mutinyhttps://archive.org/stream/MadrasSoldie ... 3/mode/2up
To prove BRUCE was in the Madras Artillery at this time, you would need to look at records not available online.
L WILSON - chaplain to 1st Bengal Light Cavalry
I doubt his claim. He is not listed as a chaplain in the followinghttps://books.google.com.au/books?id=JB ... AJ&pg=PA41
1857 East India Registerhttps://books.google.com.au/books?id=yg ... AJ&pg=PA41
1859 East India Register
The FIBIS Fibiwiki page 1st Bengal Light Cavalry and associated page 1st Bengal European Light Cavalry indicates the former regiment mutinied at Mhow.http://wiki.fibis.org/index.php/1st_Ben ... ht_Cavalryhttp://wiki.fibis.org/index.php/1st_Ben ... ht_Cavalry
If you are interested in looking at records not available online, please indicate and I will give details.