Hi,
This is really good stuff and the more information you've find just highlights what a dangerous and interesting life William must have led.
We know from your information (did you get this from any confirmed documents ?)that William saw action during the following campaigns in India and so would have been awarded the following medals:
Gwalior Campaign Stars 1843
Description:
Six-pointed star of bronze but with a silver centre bearing the name of the battle (MAHARAJPOOR or PUNNIAR) for which it is awarded and the date '29th DEC 1843'. The reverse is plain except for a pin used to attach the star to clothing. However many were later converted to take a ribbon (attached via a metal ring or one of a variety of privately fitted suspenders) in order for the star to be worn in the same manner as other medals.
Comments:
This star is made from the bronze of guns captured during the two battles of Maharajpoor and Punniar of the Gwalior campaign. Presented by the Indian government to all ranks the original issues were made with hooks on the reverse to wear the star on the breast but rings or suspenders were later fitted by recipients to allow wear in keeping with other medals.
Punjab Campaign 1848-49
Description:
The obverse of the medal bears the head of young Queen Victoria and the legend 'VICTORIA REGINA'. The reverse depicts Sir Walter Gilbert receiving the Sikh surrender with the inscription 'TO THE ARMY OF THE PUNJAB' above and the date MDCCCXLIX in the exergue below. The suspender is of the common swivelling ornate scroll type.
Comments:
A large number of these medals were awarded to Indian troops but many of them were later melted down for their silver content. As a result more examples are found for sale named to European recipients than native troops.
Indian Mutiny 1857-59
Description:
Queen Victoria with the inscription "Victoria Regina". The reverse shows Britannia with a wreath in her outstretched right hand whilst defending herself with a Union Flag covered shield on her left hand. to the right of Britannia you will see a Lion underneath the word India. At the base of the reverse you will see the dates 1857 - 1859.
Comments:
There are four different clasps that were awarded with Indian Mutiny Medal: 'DELHI' (30th May - 14th Sept 1857), 'DEFENCE OF LUCKNOW' (29th Jun - 22nd Nov 1857), 'RELIEF OF LUCKNOW' (Nov 1857), 'LUCKNOW' (Nov 1857 - Mar 1858) and 'CENTRAL INDIA' (Jan - Jun 1858).
This link gives information and photo's of all the medals awarded by the British Army so I'm afraid you'll have to search the database to find the Indian Campaign medals.
http://www.northeastmedals.co.uk (I remembered the link this time

)
These would have been the general medals awarded but depending on what engagements William was involved in during the campaign he may have been awarded clasps that were added to the medals eg. if fought at the defence of Lucknow then the clasp 'DEFENCE OF LUCKNOW' (29th Jun - 22nd Nov 1857)
would have been attached to his general Indian Mutiny 1857-59 medal. We need to find out the whereabouts of his Regiment during these campaigns to confirm what engagements he was involved.
I found this listed on the National Archive website which may have information on Williams service history but you'll need to either visit Kew or get someone to check the records. This can be expensive if you use a professional researcher and you're not sure what information will be found if any

. We know it covers the general surname Brad and the dates, pension awarded and Regiment details seem to fit.
National Archive
WO Records created or inherited by the War Office, Armed Forces, Judge Advocate General, and related bodies
Division within WO Records of the Royal Chelsea and Kilmainham Hospitals
WO 97 Royal Hospital Chelsea: Soldiers Service Documents
Subseries within WO 97 1855-1872: discharge papers arranged by regiment and range of surname. (WO 97/1272-1721)
Subsubseries within WO 97 Royal Artillery
Scope and content Royal Artillery: Brad - Bru
Covering dates 1855-1872
Availability Open Document, Open Description, Normal Closure before FOI Act: 30 years, This series is currently undergoing digitisation (from May 2008). Access to certain pieces will be disrupted over the next 3 years and advance ordering of this series may be interrupted during this time. Please check with us that the pieces that you wish to consult are not affected before you travel. For more details please visit the project news at
http://www.nationalarchives.gov.uk/news/stories/212.htm.
Held by The National Archives, Kew.
I think we know need to concentrate on William's Regiment to attempt to pinpoint the whereabouts and movements of his regiment which may not been that easy.
I think "Bhorels" were the Sikh tribe that led the revolt againts the British but I need to confirm this yet.
I think the Gwalior Campaign 1843 was small one and only comprised of 2 Brigades so we can assume William fought at the battle of MAHARAJPOOR or PUNNIAR.
Ok we're getting somewhere because I've found mention of the death of Lieutenant Henry Stanger Leathes of the Bengal Artillery at the Battle of MAHARAJPOOR and we know William was serving with the Bengal Artillery.
Lieutenant Henry Stanger Leathes - Bengal Artillery.
Memorial at St. Mary Abbotts, Kensington - "In memoriam, Henry Stanger-Leathes, Lieut. HM Regt Artillery slain in Battle of Maharjpore at the taking of the fortress of Gwalior 29th Decr 1843 aged 24. Buried on the battlefield. Son of Thos Leathes Stanger-Leathes of Dale Head Hall, Thirlmere, Cumberland."
I'll check further and get back to you with I hope more information.
Chin up we're moving in the right direction I think
Regards
Adrian