The answer to the 60th question is rather complicated, but they were a regular unit of the line from the start (and to the finish).
The original idea was to raise a regiment of four battalions to serve almost as a foreign legion garrisoning America, but that idea was quickly overtaken by events. It had men in its ranks from all over Europe, including a good number of Irish. It had a sprinkling of Swiss and German officers, including Bouquet and Haldimand. But in the end, it really was just another regular line regiment. The Mollo reference of the inspection report is not particularly helpful as it doesn't give a date or location.
The usual look for the 60th would be red coat faced blue, not lace. The leggings changed from black gaiters to wool leggins in 1759.
There are at least two know portraits of 60th officers and perhaps one of the Light Infantry.
There were likely differences of uniform between the four battalions, and even within the same battalion, as noted in the Bouquet papers where he says his men didn't have the blue wool welted button holes on their waistcoats like the rest of the troops with Stanwix.
Here is the best look at a 60th officers uniform as displayed by the then Colonel Commandant Sir Jeffrey Amherst
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The other officer portrait is that of Sir John St. Clair who exchanged battalions at some point with Haldimand.
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The Light infantryman is featured in the Sir William Johnson portrait.
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If I were painting 60th I'd give them blue breeches, blue facings, cuffs and turnbacks. Red waistcoat. Officers with silver hat lace. It is uncertain if the officers wore silver gorgets or not.